Question

Analyze the graphs of
f
(
x
)
=
|
x
|
and
g
(
x
)
=
|
5
8
x
|
. What is the correct description that takes the graph of f(x) to the graph of g(x)?(1 point)
Responses

a horizontal compression by a factor of
5
8
a horizontal compression by a factor of 5 eighths

a horizontal compression by a factor of
8
5
a horizontal compression by a factor of 8 fifths

a horizontal stretch by a factor of
5
8
a horizontal stretch by a factor of 5 eighths

a horizontal stretch by a factor of
8
5

Answer 1

To analyze the transformations between the graphs of \( f(x) = |x| \) and \( g(x) = | \frac{5}{8} x | \), we need to understand how the \( \frac{5}{8} \) factor affects the graph of \( f(x) \).

1. **Understanding the scaling factor**: The function \( g(x) = | \frac{5}{8} x | \) can be rewritten as:
\[
g(x) = \left| \frac{5}{8} x \right| = \frac{5}{8} |x|
\]
This indicates that \( g(x) \) compresses or stretches the graph of \( f(x) \) horizontally based on the coefficient inside the absolute value.

2. **Effect of \( \frac{5}{8} \)**:
- A factor of \( \frac{5}{8} \) inside the absolute value compresses the graph horizontally by the reciprocal of that factor. The reciprocal of \( \frac{5}{8} \) is \( \frac{8}{5} \).

3. **Conclusion**:
Since \( g(x) = | \frac{5}{8} x | \) can be derived from \( f(x) \) by a horizontal compression by a factor of \( \frac{8}{5} \), the correct description that takes the graph of \( f(x) \) to the graph of \( g(x) \) is:

- **A horizontal compression by a factor of \( \frac{8}{5} \)**.

Therefore, the correct response is:
- **a horizontal compression by a factor of \( 8/5 \)**.