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If the domain of f(x) is [-5,8], what is the domain of the function y = f(x+2) -1 ?

A[-7,6]
B[-3,9]
C[-4,6]
D[-7,7]
E[-3,10]

I figured that the answer was d, however the answer key states that it is a. Can you explain why?

Verified Answer :

wizard123

The domain of function f(x) is [-5,8]. So no matter what the input to "f" is, the domain still applies. 
In this case the input is "x+2", set input equal to domain to solve for x.
These x values will represent new domain for f(x+2) -1.

x+2 = -5   ----->  x = -5 -2 = -7
x+2 = 8   ------> x = 8 -2 = 6

Therefore domain is [-7,6]

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