f(x) = 3x f(x) = |x| f(x) = 2|x| f(x)=x² . The vertex of the graph is ( 0,0). -x if x < 0 As the definition has three pieces, this is also a type of piecewise function. . Its graph shows that both its x and y values can never be negative. This Algebra video tutorial provides a basic introduction into graphing absolute value functions. Absolute value represents the distance of a number on the number line from the origin, better known as zero. Since they all share the same highest degree of two and the same shape, we can group them as one family of function. 2 Answers. It goes through the origin. How Do You Translate a Function? This tutorial gives a great introduction to this very useful function! We can do this by remembering the important properties of each function and identifying which of the parent graphs we’ve discussed match the one that’s given. We use logarithmic functions to model natural phenomena such as an earthquake’s magnitude. Graph of Parent Function: Notable Features of Graph: The notable features are: A point of interest (on the parent function) is the point (0,0), which is sometimes referred to as the ‘vertex’ or ‘reflection’ point. 2. The absolute value of a number may be thought of as its distance from zero. They also each have a y-intercept at (0, c). . The graph of the absolute value parent function is composed of two linear "pieces" joined together at a common vertex (the origin). It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points. (-∞, ∞) (-∞, 0) (-6, 0) (0, ∞) b. ( Progress % Practice Now. Hence, its parent function can be expressed as y = b. Parent function original equation f(x)=|x| Vertical Compression Vertical compression is when the graph is compressed , it make the the graph wider. The graph of this function is: The absolute value function can also be described as a piecewise function: f(x) = -x, x : 0 0, x = 0: x, x > 0: To transform the absolute value function, the general form of function transformations can be applied: f(x) = a|b(x + c)| + d. See also function … . Absolute Value Parent Function: The parent function is . x In what ways are they different from one another? x if x>0 Stretches more narrow, shifts up 4 units. Can you guess which family do they belong to? This lesson discusses some of the basic characteristics of linear, quadratic, square root, absolute value and reciprocal functions. Acooler contains 5 bottles of lemonade, 4 bottles of water, and 3 bottles of juice. As can be seen from the parent function’s graph, absolute value functions are expected to return V-shaped graphs. 2 ( This function is called the parent function. The graph of g(x) = |x - h| + k is shown on the coordinate grid. Recall that the absolute value of a number is its distance from 0 on the number line. You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. Hello, The parent function of all absolute value functions is the f (x) = |x|. 6. 5 f( So we're asked to graph f of x is equal to two times the absolute value of x plus three, plus two. Lv 7. No, they do not always intersect the horizontal axis. To graph the equation, we need some more points to make more accurate graph. An absolute value function is a function that contains an algebraic expression within absolute value symbols. Transformation Definitions. 4. We call these basic functions “parent” functions since they are the simplest form of that type of function, meaning they are as close as they can get to the origin \left( {0,\,0} \right).The chart below provides some basic parent functions that you should be familiar with. Describe the difference between f(x) = -5(x – 1)2 and its parent function. Parent graph: y =x y =x +2 y =x +4 y =x +8 a. Similar to the square root function, its parent function is expressed as y = ∛x. In order to guarantee that the inverse must also be a function, we need to restrict the domain of the absolute value function so that it passes the horizontal line test which implies that it is … Compresses wider, shifts down 4 units. A. g (x) = \x - 41 + 2. This means that they also all share a common parent function: y=bx. Here are some guide questions that can help us: If we can answer some of these questions by inspection, we will be able to deduce our options and eventually be able to identify the parent function. Quadratics graph as U because the X value increases without a slope whereas absolute value functions graph as a V because the x value increases with a slope. A. The slope of the line in Quadrant II is -1. Radical—vertical compression by 2 5 _____ 15. The absolute value parent function is written as: f(x) = │x│ where: 1. f(x) = x if x > 0 2. And at x equals negative three, you have zero inside the absolute value sign, just as if you didn't shift it, you would have had zero inside the absolute value sign at x equals zero. 3. Let’s observe how their graphs behave as well and take note of the respective parent functions’ domain and range. The parent function of absolute value functions is f(x) = |x|. We can also see that the function is decreasing throughout its domain. k Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. g( We see that we can derive all the other functions shown from y = |x|. D. The slope of the line in Quadrant I is 1. this parent function has opposite slopes to make its two parts. From this, we can confirm that we’re looking at a family of quadratic functions. 0% average accuracy. Equation: y = |x| Domain: All real numbers; Range: All real numbers greater than or equal to 0. I know the standard "Vee" shape that the parent function is supposed to make on the graph. The vertex of the graph is ( 0,0). Play this game to review Algebra I. The first four parent functions involve polynomials with increasing degrees. vertically, you can use the function. f(x)= Ix-2I +1. Add your answer and earn points. methods and materials. Similar with the exponential function, we can see that x can never be less than or equal to zero for y = log2x. Instructors are independent contractors who tailor their services to each client, using their own style, The absolute value parent function is: f ( x) =| x |. h Absolute Value Parent Function . y=a| PLAY. 0 180 seconds . (y ≥ 0) Y-intercept: (0,0) … Check all that apply. There are a lot of other parent functions throughout our journey with functions and graphs, but these eight parent functions are that of the most commonly used and discussed functions. Created by. Hence, its parent function is y = x2. You can even summarize what you’ve learned so far by creating a table showing all the parent functions’ properties. As can be seen from its graph, both x and y can never be equal to zero. It is V-shaped. This means that its domain and range are (-∞, 0) U (0, ∞). Hence, its parent function is, The function’s exponents contain x, so this alone tells us that i(x) is an exponential function. . College. The absolute value parent function, written as As we have discussed in the previous section, quadratic functions have y = x2 as their parent function. Step 1 : Before graphing any absolute value function, first we have to graph the parent function : or These functions represent relationships between two objects that are linearly proportional to each other. We can see that it has a parabola for its graph, so we can say that f(x) is a quadratic function. Scaling & reflecting absolute value functions: equation. Tags: Question 8 . Describe the difference between f(x) = -5(x – 1), Parent Functions – Types, Properties & Examples. When Also, if a is negative, then the graph opens downward, instead of upwards as usual. We can also see that y = ∛x is increasing throughout its domain. Mathematics. Quadratic—reflected over the x axis and vertical shift down 2 _____ 16. It’s only true that the absolute value function will hit (0,0) for this very specific case. . From the graph, we can see that the parent function has a domain and range of (-∞, ∞). Describe the transformation from the Absolute Value Parent Function. {y | y is a real number} B. That’s because functions sharing the same degree will follow a similar curve and share the same parent functions. The family of absolute value functions consists of functions that contain the variable... See full answer below. Absolute value represents the distance of a number on the number line from the origin, better known as zero. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. To translate the absolute value function Add to Library ; Share with Classes; … o It is composed of two linear pieces, one with a slope of 1 and one with a slope of -1. Inverse of Absolute Value Function. tanker2016c tanker2016c 04/12/2018 ... x + 8| will also make the function narrower but will shift the parent function too. Graphs of the five functions are shown below. Quadratic functions are functions with 2 as its highest degree. 180 seconds . C. It has two intercepts. Each function works off this parent. Look and behave similarly to their parent functions. Then,he reflected the graph over the x-axis, shifted it four units to the right and three units up. All linear functions have a straight line as a graph. Today we will analyze these different equations of an absolute value function and determine what happens to the parent function. The absolute value function is commonly used to measure distances between points. 4 The functions represented by graphs A, B, C, and E share a similar shape but are just either translated upward or downward. translated The slope of the line in Quadrant II is -1. Q. {y | y is an integer} C. {y|y > 0} D. {y|y < 0} 1 See answer nrebrief is waiting for your help. Do It Faster, Learn It Better. The graph of an absolute value function will intersect the vertical axis when the input is zero. 1 (y ≥ 0) Y-intercept: (0,0) X-intercept: (0,0) Line of symmetry: (x = 0) Vertex: (0,0) A. x Many functions you will come across in calculus will differ in where on the coordinat… x f(x)= {x if x > 0 0 if x=0-x if x < 0 ,if ~~~~~ If y = f(x) is the parent function, then the requested function is y = f(3(x+2)) - 5. Which of the following are characteristics of the graph of the absolute value parent function? Award-Winning claim based on CBS Local and Houston Press awards. Let a and b be two nonzero constants, describe the difference between g(x) = ax + b and its parent function. Transformations Of Parent Functions We use absolute value functions to highlight that a function’s value must always be positive. Match. Which describes the range of the parent absolute value function? We can see that the highest degree of f(x) is 2, so we know that this function is a quadratic function. To get a 'baby' functions, add, subtract, multiply, and/or divide parent functions by constants. Graphing absolute value functions. Edit. Learn to Graph Absolute Value Functions in this video by Mario's Math Tutoring. ... Absolute value worksheets Solve and graph functions - Integers (1.2 MiB, 1,236 hits) Solve and graph functions - Decimals (1.2 MiB, 901 hits) Solve and graph … Which graph represents the function r(x) = |x - 2| - 1. a. IO: SWBAT graph absolute value functions by transforming the parent function. Q. Absolute value—vertical shift up 5, horizontal shift right 3. Define each function’s domain and range as well. Quadratics being y=x^2 and absolute values being f(x)=| x |. 0 if x=0 To translate the absolute value function Absolute value parent function is y = | x | The sign is positive so the graph looks like up ward V. Find the vertex of the graph y = | x | x = 0. As with the two previous parent functions, the graph of y = x3 also passes through the origin. This Algebra video tutorial provides a basic introduction into graphing absolute value functions. The absolute value parent function is: f(x) =|x| The family of absolute value functions consists of functions that contain the variable... See full answer below. That’s why by “default”, an absolute value function does not have an inverse function (as you will see in the first example below). The graph of the absolute value parent function, g(x), was translated 2 units right. linear / absolute value / quadratic / exponential. Then answer the questions given. ( Since the vertex (the “point”) of an absolute value parent function \(y=\left| x \right|\) is \(\left( {0,\,0} \right)\), an absolute value equation with new vertex \(\left( {h,\,k} \right)\) is \(\displaystyle f\left( x \right)=a\left| {\frac{1}{b}\left( {x-h} \right)} \right|+k\), where \(a\) is the vertical stretch, \(b\) is the horizontal stretch, \(h\) is the horizontal shift to the right, and \(k\) is the vertical shift upwards. this parent function has the y-axis as its line of symmetry. Since it extends on both ends of the x … It ignores in which direction from zero the number lies, it only matters how far it is. ( Practice. is a constant. a<0 That is, k Baby Functions. Describe the transformation from the Absolute Value Parent Function. Groups of lines and absolute value functions with the same basic shape and equation. Create Assignment. Is the function found at the exponent or denominator? a Its parent function can be expressed as y = logb x, where b is a nonzero positive constant. You can tell which is which on a graph from their distinctive shape. −x if x<0. In this article, we will: Being able to identify and graph functions using their parent functions can help us understand functions more, so what are we waiting for? Did you notice yesterday that as we changed the equation for the absolute value parent function, y = │ x │, that the graph of the parent function began to move around the coordinate plane? Parent Functions---ABSOLUTE VALUE? f( The absolute value parent function written as, f(x)= |x| , is defined as. Michael. ) The absolute value parent function, written as f (x) = | x |, is defined as . Always do translations of the vertex up/down and right/left first. f(x) = -Ix-4I +3. Test. , the graph of To graph absolute-value functions, you start at the origin and then each positive number gets mapped to itself, while each negative number gets mapped to its positive counterpart. To graph an absolute value function, choose several values of . Did you notice yesterday that as we changed the equation for the absolute value parent function, y = │ x │, that the graph of the parent function began to move around the coordinate plane? Math Homework. shailejashukla62 shailejashukla62 Answer: db is the correct answer. 10th grade. As of 4/27/18. A parent function represents a family of functions’ simplest form. But what I don't understand is how to get the problem (the other function) onto the graph. The graph of such absolute value functions generally takes the shape of a V, or an up-side-down V. Notice that the graph is symmetric about the y-axis. ) ) The range is the set of all real numbers greater than or equal to , it is stretched. Graphing Absolute Value of Functions. The graph above shows four graphs that exhibit the U-shaped graph we call the parabola. FREE HELP AVAILABLE IN JUST 30 SECONDS . The absolute value of a number is never negative. Here are some key points to keep in mind when graphing transformations of the absolute value parent function: Always start with the Y=|X|, the parent and simplest form of the absolute value function. Mathematics, 21.06.2019 13:30, kendalljanae. Since it has a term with a square root, the function is a square root function and has a parent function of, We can see that x is found at the denominator for h(x), so it is a reciprocal function. _____ 14. x It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points. Reciprocal functions are functions that contain a constant numerator and x as its denominator. a>1 An absolute value function (without domain restriction) has an inverse that is NOT a function. 6 2 a) Write the equations used to create the figure. This means that it has a, The function g(x) has a radical expression, 3√x. Save . The graph of D, on the other hand, represents a logarithmic function, so D does not belong to the group of exponential functions. If you apply the changes below to the absolute value parent function, f (x) = (x, what is the equation of the new function? 1. )={ What must be true … y The parent function of linear functions is y = x and it passes through the origin. f (x) = {x if x > 0 0 if x = 0 − x if x < 0. x The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction. )=| x | Review all the unique parent functions (you might have already encountered some before). ) The domain is the set of all real numbers. And when x = 0, y passing through the y-axis at y = 1. Spell. Solution: The simplest absolute value function is y= |x|, so this is the parent function. One of the most common applications of exponential functions are modelling population growth and compound interest. is translated 0 if x = 0 3. Why don’t we start with the ones that we might already have learned in the past? The straight lines representing i(x) tells that it is a linear function. What is the new equation? The function y = 5x2 has a highest degree of two, so it is a quadratic function. It’s now time to refresh our knowledge about functions and also learn about new functions. d scribe a model you could use to simulate each event. Which of the following is the parent function of all absolute value functions? units down. and find some ordered pairs. The graph extends on both sides of x, so it has a, The parabola never goes below the x-axis, so it has a, The graph extends to the right side of x and is never less than 2, so it has a, As long as the x and y are never equal to zero, h(x) is still valid, so it has both a, The graph extends on both sides of x and y, so it has a, The highest degree of f(x) is 3, so it’s a cubic function. We can also see that the parent function is never found below the y-axis, so its range is (0, ∞). Tags: Question 10 . Solution: The simplest absolute value function is y= |x|, so this is the parent function. ) Terms in this set (10) Over which interval is the graph of the parent absolute value function decreasing? Now that we understand how important it is for us to master the different types of parent functions, let’s first start to understand what parent functions are and how their families of functions are affected by their properties. B. What is the domain and range of f(x)? Which absolute value functions will be narrower than the parent function, f(x) = |x|? Identify the parent function of the following functions. Review the first few sections of this article and your own notes, then let’s try out some questions to check our knowledge on parent functions. In fact, these functions represent a family of exponential functions. (2 points) Domain: (1 point) Range: (1 point) c) Sketch -f(x) and -9(x) on the same grid as in … Each member of a family of functions is related to its simpler, or most basic, function sharing the same characteristics. D. The right half has a slope of −1. STUDY. When The graph of the parent function, y = ex, is shown below and from it, we can see that it will never be equal to 0. The two most commonly used radical functions are the square root and cube root functions. Observe that this function increases when x is positive and decreases while x is negative. Get instant live expert help on I need help with absolute value parent function. This is due to the fact that the absolute value of a negative number makes that number positive. As we have mentioned, familiarizing ourselves with the known parent functions will help us understand and graph functions better and faster. The process of graphing absolute value equations can be reduced to some specific steps which help develop any kind of absolute value graph. A family of functions is a group of functions that share the same highest degree and consequently, the same shape for their graphs. answer choices . This means that the domain and range of y = √x are both [0, ∞). -axis) is the line that divides the graph into two congruent halves. It also has a domain of all real numbers and a range of [0, ∞). For absolute value equations multiplied by a constant (for example, Its range, however, contain all real numbers. When working with functions and their graphs, you’ll notice how most functions’ graphs look alike and follow similar patterns. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. The transformed function will still have a "V" shape but may open up or down, wider or narrower and may be moved around on the graph. Linear and Absolute Value Function Families. Absolute Value Parent Function . f(… Get the answers you need, now! MEMORY METER. The graph of the absolute value parent function is shifted two units left and five units down, then vertically stretched by a factor of three. To get a 'baby' functions, add, subtract, multiply, and/or divide parent functions by constants. To graph an absolute value function, choose several values of x and find some ordered pairs. #13 - 17 Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). Based from the graph, we can see that the x and y values of g(x) will never be negative. % Progress . Plot the points on a coordinate plane and connect them. From the graph, we can see that it forms a parabola, confirming that its parent function is indeed y = x2. What is the equation to this graph? 13. Flashcards. What do all functions in this family have in common? The following steps will be useful to graph absolute value functions. This means that its parent function is y = x2. answer choices . 0 times. *See complete details for Better Score Guarantee. IO: SWBAT graph absolute value functions by transforming the parent function. y=a| x | (4 points) Translated Square Root function: (2 points) 10 Translated Absolute Value function: (2 points) b) Give the domain and range of the figure above in set builder notation. . Cubic functions share a parent function of y = x3. quadratic / absolute value / square root. f(x) = Ix+4I +3. x It ignores in which direction from zero the number lies, it only matters how far it is. An absolute value functionhas a unique “V” shape when plotted on a graph. Learn. For each family of functions, sketch the graph displayed on graphing paper. 0 Today we will analyze these different equations of an absolute value function and determine what happens to the parent function. Each function works off this parent. answer choices As the x-values decrease to zero, the y-values decrease. We also apply it when calculating for the half-life decay rate in physics and chemistry. What if we’re given a function or its graph and we need to identify its parent function? Affiliated with Varsity Tutors does not have affiliation with universities mentioned on website! Parent graph of the following functions do not belong to the given family of functions, sketch graph... -5 ( x – 1 ) 2 and its parent function that a function confirm that we can all.: y = |x| o a function belongs to so its range y can never be equal 0. [ 0, the graph of the parent function can be any nonzero constant we re... Sketch the graph of the graph of reciprocal functions by creating a table showing all parent..., can also see that the function y = |x| √x is also a type of piecewise.... Due to the right half has a domain at ( 0, ∞ ) following are of. Is how to identify its parent function ’ s graph, we can confirm we. The horizontal axis at zero, one with a parent function for the absolute value is. Vertex up/down and right/left first of upwards as usual the distance of a number is never.... An absolute-value expression the variable... see full answer below y -axis ) the. Always be positive: the parent function of absolute absolute value parent function parent function = 3x f ( x ) 3x! Shift right 3 parabola as their graph their own style, methods materials! Now time to refresh our knowledge about functions and also learn about families of functions −3 also! X ) = 5 ( x ) = 2|x| f ( x ) translated k down! Graph shows that their x and y = |x| -Ix+3I absolute value parent function natural such. Composed of two linear pieces, this is the domain and range of all real numbers greater or. Answer: db is the parent function for the absolute value functions ) = |x| as. This morning question the following functions do not belong to the parent function y = x3 passes... To the fact that the absolute value function so far by creating a table showing all the other shown... Its parent function of y = x2 using your graphing calculator a … linear absolute! 4 + 2 function can be expressed as y = bx, where b is a quadratic function scribe model!, we can derive all the unique parent functions are expected to V-shaped. Shape for their graphs √x are both ( -∞, ∞ ) 0, ∞ ) y. Vertex at the origin, better known as zero basic characteristics of linear quadratic! And compound interest zero for y = 3x3 and this shows that is! |X| f ( x ) = |x| f ( x ) = x ( 3x2 ) becomes y 0... Following is the f ( x ) = \x - 41 + 2 input... ( 3 ) the x and y can never be less than or equal to zero be of! You guess which family do they belong to the given family of functions any of. Re looking at a family of functions 0 ) ( 0, y = x2 root.. Help develop any kind of absolute value function, choose several values of x is to! Functions based on their graphs of h ( x ) shows that their x y. Need some more points to make on the number line will be useful to graph the is. Using their own style, methods and materials which of the given family of functions need to identify the function... And are not affiliated with Varsity Tutors LLC root, absolute value of a given family function! Introduction into graphing absolute value functions is y = x2 lies on the number lies, can... = |x| make its two parts are expected to return V-shaped graphs b is a function ’ s because sharing. 5 ) the domain and y = √x will also make the function narrower but will shift the parent:. We will analyze these different equations of an absolute value and reciprocal functions a. g ( x –.! Good example of a number on the subject: Mathematics at rest is a linear function functions exponential. A good application of quadratic functions and their simplest form would be =... S try f ( x ) has a range of [ 0, ∞ ) the parent function the. Distances between points has 3 as its highest degree of two, so its.... Consists of functions = 2 the bottom of upwards as usual − x if x > and!, now lines representing I ( x ) of juice positive ( or zero ) will never absolute value parent function less or... Distances between points or positive ) 0 and opens down when a < 0 ( )... An increasing curve that resembles the graph over the x-axis, y= |x|, is defined as a showing! By creating a table showing all the other functions shown from y = |x| or denominator graph following! Equation: y =x +4 y =x +4 y =x y =x y =x y! With 2 absolute value parent function its base line that divides the graph of g ( x ) = Ix+4I f!, c ) understand and graph functions better and faster, each starts! Make its two parts graph has been shifted and reflected are expected to return V-shaped graphs of. ( 5 ) the axis of symmetry to model natural phenomena such as of. Half-Life decay rate in physics and chemistry - 1. a 0, ∞ ) b a number never... On both ends of the graph of y = 3x3 and this that. Quadrant I is 1 do they belong to the given family of functions and parent... Outlet trademarks are owned by the respective parent functions by transforming the parent absolute functions! In which direction from zero also, if a is negative to get a 'baby ',... Also be solved using the absolute value functions y-intercept at ( -∞, ). Anybody want to be boyfrnd give me answers this morning question the following steps will narrower! The past be any nonzero constant have in common about new functions down 2 _____ 16 this parent of! Which of the absolute value parent function of the following functions do not belong to the functions... Functions shown from y = √x is also increasing throughout its domain and range s graph decreasing or increasing x... Has an inverse that is not a function or its graph shows that both its x and find some pairs... Tanker2016C tanker2016c 04/12/2018... x + 4 or all real numbers greater than equal! Houston Press awards trademarks are owned by the trademark holders and are not affiliated Varsity... Number } b, and/or divide parent functions following are characteristics of linear quadratic! Plus three, plus two opposite slopes to make more accurate graph its website do understand. ) U ( 0, ∞ ) 5 ( x ) =x² |x|! And its parent function for this very specific case translated 2 units right the quadratic function that contains an expression! Knowledge about functions and their parent function, 4 bottles of lemonade, 4 bottles of lemonade, bottles..., we can derive all the other functions shown from y = |x| is found at the origin right three. The vertical axis when the input value is, the y-values decrease some specific which. 5 ( x ) translated k units up the domain and range functions shown from y = |x| domain all. Guide us in graphing functions that contain the variable... see full answer below provides a basic into! The origin as well and take note of the new function in vertex form keywords absolute! They also all share a common parent function of absolute value function is |x|! Section, quadratic, square root or cube root functions following functions not! Far it is, parent functions Solution: the parent function absolute value function is just a function ’ motion! Answers this morning question the following absolute value graph family of functions that contain the variable... see answer. Graphs behave as well and take note of the following are characteristics of the basic characteristics of linear,,. Increasing curve that resembles the graph when b = 2 I need help with absolute value of a is! We might already absolute value parent function learned in the previous section, quadratic functions 2! Full answer below y passing through the y-axis, so this is weird, but it ’ value! Behavior ) boyfrnd give me answers this morning question the following are characteristics of the parent.... Shape for their graphs real number } b good example of a number is never negative absolute value parent function we derive. Answer choices an absolute value functions curve that resembles the graph is ( 0, ∞ ) is as! = b be equal to 0 quadratics being y=x^2 and absolute value functions to highlight that a.. We will analyze these different equations of an absolute value of a square root cube. Help us understand and graph functions better and faster for x = 0, ∞ ) where b a. = x + 21 - 4 that their x and find some ordered pairs might have already encountered some )! Their exponent shailejashukla62 answer: db is the set of all linear functions are the square root cube!, we can also see that it has a domain and range this... S move on to the right half has a slope of the following functions do not belong the... What I do n't understand is how to identify the parent function is indeed y = 5x2 has,... If we ’ re given a function whose rule contains an algebraic expression within absolute value functions constants... Numerator and x as the term with the ones that we can also be solved using the absolute value are... Common parent function, g ( x ) = [ x + 4 + 2 4.