Question

The function g(x) is a transformed image of the graph of f(x)=2^x. Write the equation of the transformed function g(x) in the form g(x)= b^x-h+k.

f(x)
(0,1)
(2,4)

g(x)
(-1,2)
(-3,-1)

Answer 1

2^(-1-h)+k = 2
2^(-3-h)+k = -1
solve for h and k

Of course many other values for b could have been chosen, but since only two data points were given, something had to be assumed.

Answer 2

just in case you are having trouble solving exponential equations,

eliminate k and you have

2 - 2^(-1-h) = -1 - 2^(-3-h)
3 = 2^(-1-h) - 2^(-3-h)
3 = 2^-h/2 - 2^-h/8
3 = 2^-h (1/2 - 1/8)
3 = 2^-h * 3/8
8 = 2^-h
h = -3

Then k = -2, and

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

See the graph at

http://www.wolframalpha.com/input/?i=2%5E(x%2B3)-2+for+-4+%3C+x+%3C+0