Question

The graph shows that f(x) = 3x is translated horizontally and vertically to create the function g(x) = 3x – h + k. What is the value of h?

Answer 1

The answer to H and K is 2

Answer 2

The Blue graph is the graph of
`f(x)=3^x`

Notice that the blue graph is shifted 2 units up, and 2 units right.

The 2 units shift up is clear. To notice the shift to the right. notice the slight increase of the blue graph at -2, and of the red graph at 0.



`3^x` shifted 2 units right is
`3^(x-2)` because a shift of 2 units right of any function f(x) is f(x-2).


`3^(x-2)` shifted 2 units up is
`3^(x-2)+2`


So the function of the red graph is
`g=3^(x-2)+2`


Answer: h=2, k=2