Question 1080611
as I see on your image, parent function is {{{f(x)=2^x}}}; so, your answer choices for {{{g(x)}}} are wrong, should be:

A)	{{{g(x) = 2^(x + 3) + 2	}}}
B)	{{{g(x) = 2^(x + 3) - 2	}}}
C)	{{{g(x) = 2^(x - 3) + 2}}}	
D)	{{{g(x) = 2^(x - 3) - 2}}}


the graph of {{{f(x)=2^x}}} is shifted vertically {{{2}}} units horizontally {{{3}}} units,there is no compression and no stretch

 so, your answer is C)	{{{g(x) = 2^(x-3) + 2 }}}


{{{ graph( 600, 600, -10, 10, -10, 10, 2^x, 2^(x - 3) + 2) }}}