Math Problem Statement

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

Solution

To create a function g(x)g(x) from the function f(x)=x35f(x) = |x - 3| - 5 that represents a horizontal shrink by a factor of 13\frac{1}{3}, we need to replace xx with 3x3x in the original function.

Steps:

  1. A horizontal shrink by a factor of 13\frac{1}{3} involves multiplying the input xx by the reciprocal of that factor, which is 3.

  2. So, replace xx with 3x3x in the function f(x)=x35f(x) = |x - 3| - 5.

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

g(x)=3x35g(x) = |3x - 3| - 5

This represents the horizontal shrink of the graph by a factor of 13\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 12\frac{1}{2}?
  3. What happens to the graph if we reflect f(x)f(x) across the x-axis?
  4. How would you translate the graph of f(x)f(x) 4 units to the right?
  5. What is the domain and range of g(x)=3x35g(x) = |3x - 3| - 5?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Transformations

Formulas

g(x) = |3x - 3| - 5

Theorems

Horizontal Shrink Transformation

Suitable Grade Level

Grades 9-11