(f) = |x-3|-5 Write a function g whose graph is a horizontal shrink of the graph of by a factor of 1/3

To create a function \( g(x) \) from the function \( f(x) = |x - 3| - 5 \) that represents a horizontal shrink by a factor of \( \frac{1}{3} \), we need to replace \( x \) with \( 3x \) in the original function.

### Steps:
1. A horizontal shrink by a factor of \( \frac{1}{3} \) involves multiplying the input \( x \) by the reciprocal of that factor, which is 3.
   
2. So, replace \( x \) with \( 3x \) in the function \( f(x) = |x - 3| - 5 \).

Thus, the new function \( g(x) \) becomes:

\[
g(x) = |3x - 3| - 5
\]

This represents the horizontal shrink of the graph by a factor of \( \frac{1}{3} \).

Would you like more details or have any questions?

---

Here are 5 related questions for practice:

1. What would the graph look like for a horizontal stretch by a factor of 2?
2. How would you write a vertical shrink by a factor of \( \frac{1}{2} \)?
3. What happens to the graph if we reflect \( f(x) \) across the x-axis?
4. How would you translate the graph of \( f(x) \) 4 units to the right?
5. What is the domain and range of \( g(x) = |3x - 3| - 5 \)?

**Tip:** For horizontal transformations, always adjust the input value by multiplying inside the function.

(f) = |x-3|-5 Write a function g whose graph is a horizontal shrink of the graph of f by a factor of 1/3

Learn how to perform a horizontal shrink transformation on the function f(x) = |x - 3| - 5 by a factor of 1/3. This problem covers key algebraic concepts related to function transformations, making it ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation