Math Problem Statement

Describe how the graph of g(x) is related to the graph of the parent function.

g(x)=||−2x||

vertical translation: 1 of 4. Select Choice

horizontal translation: 2 of 4. Select Choice

dilation: 3 of 4. Select Choice

reflection: 4 of 4. Select Choice

Solution

The function g(x)=2xg(x) = | -2x | is a transformation of the parent function f(x)=xf(x) = |x|, which is the absolute value function.

Here's how the transformations apply:

  1. Reflection: Since there is a negative sign in front of the 2x2x, it reflects the graph over the y-axis. However, because this function is within an absolute value (which negates the effect of a reflection over the y-axis), it does not actually change the shape visually on the positive or negative sides.

  2. Dilation: The factor 22 in 2x-2x causes a horizontal compression. This means the graph of g(x)g(x) is "squeezed" horizontally by a factor of 12\frac{1}{2} compared to f(x)=xf(x) = |x|. This makes it steeper than the original parent function.

So, the correct answer is dilation due to the factor of 2, which compresses the graph horizontally.

Would you like more details, or have any questions?


Here are 5 questions to further explore this topic:

  1. How does a positive constant multiplier affect the dilation of the absolute value function?
  2. What would happen if the function were g(x)=12xg(x) = | \frac{1}{2}x |?
  3. How would adding a constant outside the absolute value affect the graph?
  4. If we applied a vertical reflection, how would that affect the graph of g(x)g(x)?
  5. How would the graph change if we shifted g(x)g(x) horizontally?

Tip: When you see a constant multiplied by xx inside an absolute value function, it typically indicates a horizontal stretch or compression.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Absolute Value Functions
Transformations
Reflection
Dilation

Formulas

g(x) = |−2x|
f(x) = |x|

Theorems

-

Suitable Grade Level

Grades 9-10