Question

If the graph of f(x) = 6x is shifted 2 units up, then what would be the equation of the new graph?
A. g(x) = 6(x - 2)
B. g(x) = 6x - 2
C. g(x) = 6x + 2
D. g(x) = 6(x + 2)

Answer 1

When you do a vertical shift...it simply means you are adding (or subtracting) a number from the whole function.

In this case...you are shifting up 2 units...so you add to the to WHOLE function...not just the x

So for this example...your answer would be C

See why?

Answer 2

Adding to or subtracting from the result of a function moves the graph up or down. Multiplying or dividing the result blows it up or shrinks it.

Adding to or subtracting from the argument (input) of the function moves the graph right or left. Multiplying or dividing the argument expands or contracts the scale along the x axis. Hopefully the attached images will help you get a good feel for this.