Question

The graph of f(x)=3•2^x -3 is shown below. G(x) is a transformation of f(x). How would you write the equation for the function g(x)?

Answer 1

C

Explanation:

To find the appropriate equation, notice the red graph has shifted up about 6 units. This means that
`3*2^x-3` which is shifted by -3 will move 6 up. -3+6= 3. This means the function will have +3. Only B and C are options. Now test a point. Notice the red function crosses the y-axis at about 5 or 6 when x=0.

`g(x) = 2^x+3\\g(0) = 2^0+3\\g(0)=1+3\\g(0)=4`

This function doesn't match.

`f(0) = 3*2^0+3\\f(0) = 3*1+3\\f(0)=6`

This function matches. Option C is correct.