Question

Which of the following describes transformation(s) of the function g(x)=|−53x|
?(1 point)
Responses

a horizontal compression by a factor of 35
a horizontal compression by a factor of Start Fraction 3 over 5 End Fraction

a horizontal stretch by a factor of 53
a horizontal stretch by a factor of Start Fraction 5 over 3 End Fraction

a reflection across the y-axis and a horizontal stretch by a factor of 53
a reflection across the y -axis and a horizontal stretch by a factor of Start Fraction 5 over 3 End Fraction

a reflection across the y-axis and a horizontal compression by a factor of 35

Answer 1

To analyze the function \( g(x) = | -53x | \), let's break it down:

1. **Reflection across the y-axis**: The negative sign in front of \( 53x \) indicates a reflection over the y-axis. This is because \( g(x) = |-53x| \) is equivalent to \( |53(-x)| \), which means the transformation reflects points horizontally across the y-axis.

2. **Horizontal compression**: The coefficient \( 53 \) in \( | -53x | \) indicates a horizontal compression by a factor of \( \frac{1}{53} \). More specifically, if we consider the general function \( g(x) = |k x| \), where \( k > 1 \), this represents a horizontal compression by a factor of \( \frac{1}{k} \). In this case, \( k = 53 \), so we have a horizontal compression by a factor of \( 53 \).

Therefore, the function \( g(x) = | -53x | \) can be described as:
- a reflection across the y-axis
- a horizontal compression by a factor of \( 53 \)

Among the response choices, the correct option is:

**a reflection across the y-axis and a horizontal compression by a factor of 53.**