Write a function  g  whose graph represents a reflection in the y-axis followed by a translation 3 units to the right of the graph of  f(x)=|x|

To create a function \( g(x) \) that represents a reflection in the y-axis followed by a translation 3 units to the right of the graph of \( f(x) = |x| \), we can follow these steps:

### 1. Reflect the graph in the y-axis:
Reflecting the function \( f(x) = |x| \) in the y-axis results in the function \( f(-x) = |-x| = |x| \). Since \( |x| \) is an even function, reflecting it over the y-axis does not change its appearance. So after the reflection, the function is still \( |x| \).

### 2. Translate the graph 3 units to the right:
To translate the graph 3 units to the right, replace \( x \) in the function with \( x - 3 \). Thus, the translated function is \( f(x - 3) = |x - 3| \).

### Final Function:
The final function \( g(x) \) is:
\[
g(x) = |x - 3|
\]

This function represents the graph of \( f(x) = |x| \) reflected in the y-axis and then translated 3 units to the right.

---

Do you want more details or have any questions? 

Here are 5 related questions:
1. How would the graph of \( f(x) = |x| \) change if reflected over the x-axis instead?
2. What would be the equation if the graph was translated 3 units to the left instead?
3. How does a vertical translation affect the function \( f(x) = |x| \)?
4. Can you describe the transformations needed to shift \( f(x) = |x| \) 2 units down and 4 units to the left?
5. What is the effect of multiplying the function \( f(x) = |x| \) by a negative constant?

**Tip:** When reflecting a function over the y-axis, always replace \( x \) with \( -x \) in the function.

Explore the graph of g(x) = |x - 3|, which represents a reflection in the y-axis followed by a translation 3 units to the right of the graph of f(x) = |x|. Understand the transformations involved in reflecting a function over the y-axis and translating it horizontally. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation