Question

Consider function f below. f(x)=4^x-6 Determine function g which is created by shifting the graph of function f up 5 units.

A.
g(x) = 4x + 5
B.
g(x) = 4(x + 5) - 6
C.
g(x) = 4x - 1
D.
g(x) = 9x - 6

Answer 1

Answer: Option C

`g(x) = 4 ^ x-1`

Explanation:

If we have a function f(x) and we want to move its graph vertically then we apply the transformation:

`g (x) = f (x) + k.`

So:

If
`k> 0` the function g(x) will be the function f(x) displaced k units up

If
`k <0` the function g(x) will be the function f(x) displaced k units down.

In this case we know that the graph of f(x) moves 5 units up.

then
`k> 0` and
`k = 5`

Therefore
`g (x) = f(x) +5`

`g(x) = 4 ^ x - 6 +5\\\\g(x) = 4 ^ x-1`