Question

Given the function f(x) = x2 and k = -3, which of the following represents a vertical shift? (2 points)

f(x) + k

kf(x)

f(x + k)

f(kx)

Answer 1

Answer: f(x) + k

Proof of validity is shown below.

Answer 2

Answer:
f(x) + k

Step-by-step explanation:
Vertical shift is represented by adding/subtracting a constant from the original given equation.
If the constant added is +ve, this means that the curve is vertically shifted upwards
If the constant added is -ve, this means that the curve is vertically shifted downwards.

Now, for the given, we have the original function f(x) and the constant k, therefore, to shift the graph vertically, the new function would be f(x)+k
We have:
f(x) = x² and k = -3
This means that the new function would be:
x² - 3
Since the constant is -ve, we can conclude that the curve is shifted vertically downwards by 3 units

Hope this helps :)