Question

Given the function f(x) = x2 and k = 3, which of the following represents the graph becoming more narrow?

Answer 1

A. f(x)+k
B. kf(x)
C. f(x+k)
D. f(x-k)

Answer 2

The only type of transformation that can make a graph more narrow/wide is a scaling transformation. A scaling transformation involves a multiple factor.

Answer 3

Shifts, whether vertical or horizontal, do not change the scale of the graph. Here, you have A representing a vertical shift, and C,D representing horizontal shifts.

Answer 4

Only B represents a vertical scale.

Answer 5

Thank you for your thorough and prompt response!

Answer 6

Yes, the answer is correct, but I want to add something to this. Just to give you more information (like a reference guide)

whenever we are presented with
f(x)+k it means that we are shifting up k units. The + sign means up
f(x)-k it means that we are shifting down k units. The - sign means down.

Now suppose we are given
f(x+k)
now that we have the parenthesis involved it means that we are either shifting k units left or right. Due to the addition sign, we are shifting k units to the left
f(x-k)
Due to the addition sign, we are shifting k units to the right

Therefore, any function given without the parenthesis means that we are either going down or up (depending on the sign) , and any function with the parenthesis means that we are either going left or right. (depending on the sign).