Question

Analyze the effect on the graph from f(x)=|x|
to g(x)=|3x|
.(1 point)
Responses

vertical compression by a factor of 13
vertical compression by a factor of 1 third

horizontal compression by a factor of 13
horizontal compression by a factor of 1 third

horizontal stretch by a factor of 3
horizontal stretch by a factor of 3

vertical stretch by a factor of 3
vertical stretch by a factor of 3

Answer 1

To analyze the effect on the graph when transitioning from \( f(x) = |x| \) to \( g(x) = |3x| \), we need to understand how the transformation affects the shape of the graph.

1. **Understanding the functions:**
- \( f(x) = |x| \) is the standard absolute value function, which has a V-shape with its vertex at (0, 0).
- \( g(x) = |3x| \) modifies the input \( x \) by multiplying it by 3.

2. **Transformation explanation:**
- When you replace \( x \) with \( 3x \) in the function, you are applying a **horizontal compression**. This means that the graph of \( g(x) \) will be squeezed towards the y-axis compared to \( f(x) \).
- Specifically, because of the factor of 3, for every x-value in \( f(x) \), \( g(x) \) reaches the same y-value when \( x \) is \( \frac{x}{3} \). Thus, the change is a horizontal compression by a factor of \( \frac{1}{3} \).

Based on this analysis, the correct response is:

**horizontal compression by a factor of 1 third.**