Answer: C) 1
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Work Shown:
I'm assuming you meant to write [tex]f(x) = 2^{x+4}[/tex] 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,
[tex]g(x) = f(x-5)\\\\g(x) = 2^{x-5+4}\\\\g(x) = 2^{x-1}\\\\[/tex]
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.
