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 value of h is:

2

Explanation:

We are given the graph of the parent function as:

`f(x)=3^x`

and the the transformed function g(x) is given by:

`g(x)=3^(x-h)+k`

The function g(x) represents that the original function f(x) is shifted h units to the right and k units upward.

This means that any point on the function f(x) i.e. (x,y) is transformed to (x+h,y+k)

The point (0,1) is transformed to (2,3)

i.e.

(0+h,1+k) =(2,3)

i.e.

(h,k+1)=(2,3)

i.e.

h=2 and k=2

Hence, the value of h is: 2

The function g(x) is given by:

`g(x)=3^(x-2)+2`

Answer 2

Each of the marked points appears to be translated 2 units right and 2 units up. Both h and k are 2.

The value of h is 2.