Question

Analyze the effects on the graph of f(x)=1x
. What changes take place when it is replaced by the function −13f(x)
?(1 point)
Responses

It vertically compresses by a factor of −13
.
It vertically compresses by a factor of negative Start Fraction 1 over 3 End Fraction .

It reflects over the y-axis.
It reflects over the y -axis.

It reflects over the x-axis and vertically stretches by a factor of 3.
It reflects over the x -axis and vertically stretches by a factor of 3.

It reflects over the x-axis and vertically compresses by a factor of 13
.

Answer 1

To analyze the effects of replacing the function \( f(x) = x \) with the function \( -13f(x) \):

1. The negative sign in front of the function indicates that the graph will be reflected over the x-axis.
2. The factor of 13 indicates a vertical stretch by a factor of 13.

Putting this together, the transformation involves reflecting the graph over the x-axis and then vertically stretching it by a factor of 13.

Therefore, the correct response from your options is:

**It reflects over the x-axis and vertically stretches by a factor of 13.**