Question

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

Answer 1

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