Math Problem Statement

What kind of transformation converts the graph of f(x) = -6|x - 2| - 3 into the graph of g(x) = -3|x - 4| - 3?

Solution

To determine the transformation that converts the graph of f(x)=6x23f(x) = -6|x - 2| - 3 into the graph of g(x)=3x43g(x) = -3|x - 4| - 3, we can break it down step by step:

Step 1: Analyze Vertical Transformation

  • In f(x)f(x), the coefficient of the absolute value is 6-6.
  • In g(x)g(x), the coefficient of the absolute value is 3-3.
    • This change from 6-6 to 3-3 represents a vertical shrink because the magnitude of the coefficient decreases (making the graph less steep).

Step 2: Analyze Horizontal Transformation

  • In f(x)f(x), the horizontal shift is x2x - 2, indicating a shift 2 units to the right.
  • In g(x)g(x), the horizontal shift is x4x - 4, indicating a shift 4 units to the right.
    • This shows a horizontal shift of 2 units further to the right, but that doesn't affect the question choices.

Step 3: Conclusion

The primary transformation between the two functions is the change in the vertical scaling from 6-6 to 3-3, which is a vertical shrink.

Thus, the correct answer is vertical shrink.

Would you like further details or have any additional questions?

Related Questions:

  1. What would a horizontal stretch look like in this context?
  2. How does a vertical reflection affect the graph of a function?
  3. Can you explain how shifting impacts the domain of absolute value functions?
  4. What would happen if we changed the constant outside the absolute value expression?
  5. How do horizontal shifts differ from horizontal stretches in terms of function transformation?

Tip:

When the coefficient inside the absolute value changes, it affects horizontal transformations, while changes outside affect vertical transformations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Transformations
Absolute Value Functions

Formulas

y = a|x - h| + k

Theorems

Transformation properties of functions

Suitable Grade Level

Grades 9-12