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The graph above is a transformation of the function f(x) = Write an equation for the function graphed above g(x) = | x − 1| X |x|

The graph above is a transformation of the function f(x) = Write an equation for the function graphed above g(x) = | x − 1| X |x|

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 20E
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My answer was wrong, im not sure how to do this. thank you!

6 5 4 3 2 7 -6 -5 -4 -3 -2 -1 1 2 3 4 6 --1 -2 -3 -4 -5 -6 The graph above is a transformation of the function f(x) = |x| Write an equation for the function graphed above g(x) = |x − 1| X
Transcribed Image Text:6 5 4 3 2 7 -6 -5 -4 -3 -2 -1 1 2 3 4 6 --1 -2 -3 -4 -5 -6 The graph above is a transformation of the function f(x) = |x| Write an equation for the function graphed above g(x) = |x − 1| X
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### Transformation of the Absolute Value Function **Graph Explanation:** The graph provided is a modification of the function \( f(x) = |x| \). - The original function \( f(x) = |x| \) is an absolute value function, which forms a symmetric V-shape with its vertex at the origin (0,0). - In the transformed graph, the vertex of the V-shape has moved to the point (-1, 1). **Finding the Equation:** The transformed function can be found by identifying the changes made to the original absolute value function. **Vertical and Horizontal Shifts:** - The horizontal shift: The transformation shifts the vertex of the graph one unit to the left, which suggests \( x \) is replaced by \( x + 1 \) inside the absolute value. - The vertical shift: The transformation shifts the vertex of the graph one unit upwards, which suggests adding 1 to the entire function. Given these transformations, the transformed function is: \[ g(x) = |x + 1| + 1 \] **Validation of Equation:** The provided options include two functions. The function that matches the transformations is: \[ \boxed{|x + 1| + 1} \] The incorrect option is: \[ \frac{1}{2}|x + 1| + 1 \] Hence, the correct equation for the transformed function is \( g(x) = |x + 1| + 1 \).
Transcribed Image Text:### Transformation of the Absolute Value Function **Graph Explanation:** The graph provided is a modification of the function \( f(x) = |x| \). - The original function \( f(x) = |x| \) is an absolute value function, which forms a symmetric V-shape with its vertex at the origin (0,0). - In the transformed graph, the vertex of the V-shape has moved to the point (-1, 1). **Finding the Equation:** The transformed function can be found by identifying the changes made to the original absolute value function. **Vertical and Horizontal Shifts:** - The horizontal shift: The transformation shifts the vertex of the graph one unit to the left, which suggests \( x \) is replaced by \( x + 1 \) inside the absolute value. - The vertical shift: The transformation shifts the vertex of the graph one unit upwards, which suggests adding 1 to the entire function. Given these transformations, the transformed function is: \[ g(x) = |x + 1| + 1 \] **Validation of Equation:** The provided options include two functions. The function that matches the transformations is: \[ \boxed{|x + 1| + 1} \] The incorrect option is: \[ \frac{1}{2}|x + 1| + 1 \] Hence, the correct equation for the transformed function is \( g(x) = |x + 1| + 1 \).
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