Question

Analyze the graphs of
f
(
x
)
=
|
x
|
and
h
(
x
)
=
7
4
|
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
7
4
a vertical compression by a factor of 7 fourths

a vertical compression by a factor of
1
4
a vertical compression by a factor of 1 fourth

a vertical stretch by a factor of
7
4
a vertical stretch by a factor of 7 fourths

a vertical stretch by a factor of 7

Answer 1

To analyze the relationship between the graphs of the functions \( f(x) = |x| \) and \( h(x) = \frac{7}{4}|x| \), we note that the function \( h(x) \) can be expressed as:

\[
h(x) = \frac{7}{4} f(x)
\]

This indicates that the graph of \( h(x) \) is derived from the graph of \( f(x) \) by multiplying the output (the height of the graph) by the factor \( \frac{7}{4} \).

When we multiply a function by a factor greater than 1, it results in a vertical stretch of the graph. Specifically, since \( \frac{7}{4} \) is greater than 1, we see that every output value of \( f(x) \) is being stretched vertically by a factor of \( \frac{7}{4} \).

Thus, the correct description that takes the graph \( f(x) \) to the graph of \( h(x) \) is:

**a vertical stretch by a factor of \( \frac{7}{4} \)**.