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

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

havimg that h=1. We get that

$k=-(\frac{1}{2})^{1-1}=-1$

so k=-1 and h=1