Answer: [tex]g(x) = 2^x - 3[/tex]
The -3 is not in the exponent
Explanation:
The parent function is [tex]f(x) = 2^x[/tex]. Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.
[tex]g(x) = f(x) - 3\\\\g(x) = 2^x - 3[/tex]
You could look at other points as well, but I find working with x = 0 is easiest.
As a check, plugging x = 0 into g(x) leads to...
[tex]g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2[/tex]
This confirms our answer.
