Question

The graph of g(x) is a transformation of the graph of f(x)=2x. Enter the equation for g(x) in the box. g(x) =

Answer 1

Answer:  $g(x) = 2^x - 3$

The -3 is not in the exponent

Explanation:

The parent function is $f(x) = 2^x$. 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.

$g(x) = f(x) - 3\\\\g(x) = 2^x - 3$

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...

$g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2$

This confirms our answer.