Question

Analyze the graphs of f(x)=|x|
and h(x)=74|x|
. What is the correct description that takes the graph f(x)
to the graph of h(x)
?(1 point)
Responses

a vertical compression by a factor of 74
a vertical compression by a factor of 7 fourths

a vertical stretch by a factor of 7
a vertical stretch by a factor of 7

a vertical stretch by a factor of 74
a vertical stretch by a factor of 7 fourths

a vertical compression by a factor of 14

Answer 1

To analyze the graphs of \( f(x) = |x| \) and \( h(x) = 74|x| \), we need to understand how the transformation from \( f(x) \) to \( h(x) \) affects the graph.

1. **Starting with \( f(x) = |x| \)**:
- This function is a V-shaped graph centered at the origin, with slopes of 1 and -1.

2. **Now looking at \( h(x) = 74|x| \)**:
- This function modifies \( f(x) \) by multiplying the output of \( f(x) \) (which is \( |x| \)) by 74.

When a graph is transformed by multiplying the output (the y-values) by a factor greater than 1, it results in a vertical stretch. In this case, since we are multiplying by 74, the graph of \( h(x) \) will be stretched upwards compared to \( f(x) \).

Thus, we can conclude:
- The graph of \( h(x) = 74|x| \) is a vertical stretch of the graph of \( f(x) = |x| \) by a factor of 74.

Therefore, the correct response is:

**a vertical stretch by a factor of 74.**