The function ƒ (x) is modified as follows: It is multiplied by - 3. x is replaced by x + 3. The new function is graphed. Which of the following effects on the graph of ƒ (x) are needed to produce the new graph? Choose all that apply.

horizontal translation

vertical translation

dilation

reflection over the x-axis

reflection over the y-axis

First the function f (x) is multiplied by - 3. This involves 2 changes:

a) Multiplication by 3

This implies dilation

b) Multiplication by - 1

This implies reflection of function over x-axis

Next x is replaced by x + 3. This means the function is shifted to left by 3 units.

So this overall transformation results in following 3 changes:

Horizontal Translation, Dilation and Reflection along x-axis