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


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

Here's how the transformations apply:

1. **Reflection:** Since there is a negative sign in front of the \(2x\), 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 \(2\) in \( -2x \) causes a horizontal compression. This means the graph of \( g(x) \) is "squeezed" horizontally by a factor of \(\frac{1}{2}\) compared to \( f(x) = |x| \). 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?

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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 \( g(x) = | \frac{1}{2}x | \)?
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 \( g(x) \)?
5. How would the graph change if we shifted \( g(x) \) horizontally?

**Tip:** When you see a constant multiplied by \(x\) inside an absolute value function, it typically indicates a horizontal stretch or compression.

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

Explore how the graph of g(x) = |−2x| is transformed from the parent function f(x) = |x|. Learn about the effects of dilation and reflection on absolute value functions, with a detailed breakdown for Grades 9-10.

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