Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with f(−3x)?

A) vertical reflection over x-axis and vertical stretch
B) vertical reflection over x-axis and vertical compression
C) horizontal reflection over y-axis and horizontal stretch
D) horizontal reflection over y-axis and horizontal compression

Answer 1

D) horizontal reflection over y-axis and horizontal compression

Explanation:

Replacing x with -x will reflect a graph across the y-axis.

Multiplying x by 3 before the function is applied will compress the graph horizontally.

This means the correct choice is D.

Answer 2

D

horizontal reflection over y-axis and horizontal compression

This is because plugging in 10 for x becomes

the - negative indicates the x has changed signs (flipped)

the 3 indicates that there will be a shrink

these shifts are learned by observing graph changes or memorization