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

a vertical compression by a factor of 14
a vertical compression by a factor of 1 fourth

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

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

Answer 1

To analyze the relationship between the graphs of \( f(x) = |x| \) and \( h(x) = 74|x| \), we can look at how the second function is derived from the first one.

The function \( h(x) = 74|x| \) can be seen as a transformation of \( f(x) \) by multiplying the output of \( f(x) \) by 74. This means that for every value of \( x \), the value of \( h(x) \) is 74 times larger than that of \( f(x) \).

This transformation suggests that there is a vertical stretch of the graph of \( f(x) \) by a factor of 74. Therefore, to get from the graph of \( f(x) = |x| \) to the graph of \( h(x) = 74|x| \), we apply:

### A vertical stretch by a factor of 74.

So the correct response is:

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