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

you don't need to know the value of k to answer this question.

you know that when you have y=f(x) you get certain y-coordinates, but when you add k
(like this: y=f(x)+k) then you know that for each x-coordinate you get an output +k greater than in a case of y=f(x), and that means that f(x)+k is a shift up)

Answer 2

(for k<0. tho' , like in your case where x=-3, it is a shift down)

Answer 3

For any parent function y=f(x), the rule is:

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VERTICAL SHIFTS

y=f(x)+c
shift c units up

y=f(x)-c
shift c units down
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SIDE SHIFTS

y=f(x-c)
shift c units to the right

y=f(x+c)
shift c units to the left
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