Question

Given the function f(x) = x2 and k = –3, which of the following represents a vertical shift? A. f(x) + k
B. kf(x)
C. f(x + k)
D. f(kx)

Answer 1

when you are dealing with any function f(x)=x^w,

a vertical shift is:
f(x) = x^w+c (shift up)

therefore the answer is:  A. f(x) + k

Answer 2

Given the function $f(x) = x^2$ and k = –3, consider all options:

A. $f(x)+k=x^2-3$ - this is translation down 3 units;

B. $kf(x)=-3x^2$ - this is reflection across the x-axis and stretch in the y-direction;

C. $f(x+k)=(x-3)^2$ - this is translation 3 units to the right;

D. $f(kx)=(-3x)^2$ - this is compression it in the x-direction.

The only possible option with vertical shift is option A.