Describing Transformations of Absolute Value Functions

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Transformations of Absolute Value Functions Graph the following absolute value functions using your graphing calculator. Without using your graphing calculator describe the transformations of the parent function.


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This fascinating concept allows us to graph many other types of functions like squarecube root exponential and.

. In Algebra 1 students reasoned about graphs of absolute value and quadratic functions by thinking of them as transformations of the parent functions x and x². Vertical compression by a factor of 13 or horizontal stretch by a factor of 3 Equation. Alignment with 2007 Mississippi Mathematics Framework Revised.

For this activity the students should be placed in groups of two or three. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Transformations of Absolute Value Functions Texas Gateway.

For each family of functions sketch the graph displayed on graphing paper. Transformation that decreases the distance between corresponding points of a graph and a line. Describe the transformation from the Absolute Value Parent Function.

Up to 10 cash back The stretching or compressing of the absolute value function y x is defined by the function y a x where a is a constant. Learn about graphing absolute value equations. DOK 2 Suggestions for Grouping.

Y x y x 2 y x 4 y x 8 a. Section 12 Transformations of Linear and Absolute Value Functions 13 Writing Refl ections of Functions Let fx x 3 1. Transformations y -a x h k Remember that h k is your vertex Reflection across the x-axis Vertical Stretch a 1 makes it narrower OR Vertical Compression 0 a 1 makes it wider Horizontal Translation opposite of h Vertical Translation Example 1.

Sketch and describe transformations of quadratic and absolute value functions. Given an absolute value function the student will analyze the effect on the graph when fx is replaced by afx fbx fx c and fx d for specific positive and negative real values. Graphing a Standard Absolute Value Graph.

Students match each function card to its graph card and transformations card. Recall that in its basic form the absolute value function is one of our toolkit functions. Understanding Absolute Value.

The transformation from the first equation to the second one can be found by finding a a h h and k k for each equation. Y x-hk is the general form of an absolute value equation. To create the following functions.

Transformations of Absolute Value Functions Matching is an interactive and hands on way for students to practice matching absolute value functions to their graphs and transformations. In this unit we extend this idea to include transformations of any function whatsoever. Equation Description of Transformation in words Domain Range II.

Transformations of Absolute Value Functions. Then answer the questions given. Vertical shift down 9 units.

9th - 12th grade. Y 3 x 2 - 3 y x 1 2 y 2 x 3 - 1 y -13x 2 1 Example 2. Vertical Stretch of 2.

F x 2x - 1 - 9. An absolute value equation is an equation having the absolute value sign and the value of the equation is a. Vertical stretch by a factor of 3 or a horizontal.

What do all functions in this family have in common. We can combine both of these translations into one problem and graph things like yx24. Write a function h whose graph is a refl ection in the y-axis of the graph of f.

1 3 or 1 3 Vertex. Stretch A stretch is a transformation. Learn how to graph absolute value equations when we have a value of b other than 1.

Absolute value functions and transformationsnotebook 17 October 14 2014 Oct 12350 PM Multiple Transformations In general the graph of an absolute value function of the form y ax h k can involve translations reflections stretches or compressions. Write an equation for the absolute function described. B will affect our horizontal shift as well as horizontal stretch compr.

Y x y x. Vertical Stretch vertical shift up 4 units. The graph opens up if a 0 and opens down when a 0.

Also if a is negative then. Algebraically for whatever the input value is the output is the value without regard to sign. In a rational function an excluded value is any x -value that makes the function value y undefined.

Factor a 1 1 out of the absolute value to make the coefficient of x x equal to 1 1. F x x f x x gx x 5 g x x - 5. Write a function g whose graph is a refl ection in the x-axis of the graph of f.

Up to 24 cash back Parent function. Students have usually seen linear quadratic and absolute value functions in Algebra 1 but the absolute value function is the first one that I really hit hard as a parent function. The domain and range is the set of all real numbers except 0.

Find the vertex domain range and describe each transformation for the absolute value function. Graph and give the domain and range. F x 2x 1 - 9.

Write an absolute value function given the following transformations. IXL - Transformations of absolute value functions Algebra 2 practice SKIP TO CONTENT. X 0 Parent function.

The parent function y x. This activity can be used in a var. First I review solving absolute value equations.

A refl ection in the x-axis changes the sign of each output value. LABEL 3 points on your graph. Y axhk y a x - h k.

The absolute value function is usually the first parent function that is taught in Algebra 2. General form of the absolute value function a function of the form fx a0x-h0 k Reflection A reflection is a transformation that flips a graph across a line such as the x- or y-axis. Transformations of Absolute Value Functions DRAFT.

Equation Description of Transformation in words Domain Range III. Do log functions have y. For absolute value equations multiplied by a constant for example y a x if 0 a 1 then the graph is compressed and if a 1 it is stretched.

The parent function of a rational function is fx1x and the graph is a hyperbola. To graph an absolute value function start by. Horizontal shift left 1 unit.


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