Question

The graph of f(x) = 2^x + 4 shifts five units to the right when it is replaced with the graph of f(x) = 2^x - k. what is the value of k?

A. 5

B. -1

C. 1

D. 4​

Answer 1

Answer: C) 1

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Work Shown:

I'm assuming you meant to write
`f(x) = 2^(x+4)` where all of the "x+4" is the exponent.

If we shift f(x) 5 units to the right to end up with g(x), then,

`g(x) = f(x-5)\\\\g(x) = 2^(x-5+4)\\\\g(x) = 2^(x-1)\\\\`

In the second step, I replaced every copy of x with x-5 so that I could apply the translation of 5 units to the right.

The exponent for g(x) is x-1, which matches up with x-k. We see that k = 1.