My answer was wrong, im not sure how to do this. thank you! 654327-6 -5 -4 -3 -2 -11 2 3 46--1-2-3-4-5-6The graph above is a transformation of the function f(x) = |x|Write an equation for the function graphed aboveg(x) =|x − 1|X

Given: The graph is shown below. The above graph is a transformation of the function fx=x. The…

Answered: The graph above is a transformation of…

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|

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 12RE: The graph below shows transformations of the graph of f(x)=2x. What is the equation for the...

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Question

My answer was wrong, im not sure how to do this. thank you!

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-6 -5 -4 -3 -2 -1
1 2 3 4
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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 \( g(x) = |x + 1| + 1 \).

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