Question

The graph below is a transformation off(x) = -(1/2)^x Write a function that represents the graph.g(x) = (1/2)^x-h +kh=k=

Answer 1

we get that g(0)=1 and g(1)=0. Therefore

`\begin{gathered} ((1)/(2))^(-h)+k=1 \\ ((1)/(2))^(1-h)+k=0\rightarrow k=-((1)/(2))^(1-h) \\ ((1)/(2))^(-h)-((1)/(2))^(1-h)=1 \\ 2^h-2^(h-1)=1 \\ 2^h(1-(1)/(2))=1 \\ 2^{h^{}}((1)/(2))=1 \\ 2^h=2\rightarrow h=1 \end{gathered}`

havimg that h=1. We get that

`k=-((1)/(2))^(1-1)=-1`

so k=-1 and h=1