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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

User Schankam
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1 Answer

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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

User Csinchok
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