Question

Analyze the graphs of f(x)=|x|
and g(x)=|58x|
. 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 58
a horizontal compression by a factor of 5 eighths

a horizontal compression by a factor of 85
a horizontal compression by a factor of 8 fifths

a horizontal stretch by a factor of 58
a horizontal stretch by a factor of 5 eighths

a horizontal stretch by a factor of 85

Answer 1

To analyze the graphs of \(f(x) = |x|\) and \(g(x) = |58x|\), we focus on how the graph of \(f(x)\) is transformed to obtain the graph of \(g(x)\).

The function \(g(x) = |58x|\) can be rewritten as \(g(x) = |58| \cdot |x|\). Here, we are scaling the input \(x\) by a factor of 58. The effect of multiplying \(x\) by a constant (greater than 1) inside the absolute value function results in a horizontal compression.

1. **Horizontal Compression**: If you have a function \(f(x)\) and you create \(g(x) = f(kx)\) where \(k > 1\), this induces a horizontal compression of the graph by a factor of \( \frac{1}{k} \).

In this case, \(k = 58\). Thus, \(g(x)\) can be seen as applying a horizontal compression of the graph of \(f(x)\) by a factor of \( \frac{1}{58} \).

To summarize:
- The function \(g(x) = |58x|\) represents a horizontal compression of the graph of \(f(x) = |x|\) by a factor of \( \frac{1}{58} \), or equivalently, it is a horizontal compression by a factor of 58.

Taking this into account, the correct description is:
**a horizontal compression by a factor of **58**.**