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.

Answer 1

Answer: Option C

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

Step-by-step 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 $k$ 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 $g (x) = f(x) +5$

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