Question

The function f(x)=4∙2^x is graphed to the right. Sketch a graph of the function g(x) represented by the rule g(x)=f(x-2)+3. Mark the asymptote to help make your graph clear.

Answer 1

Given:

`f(x)=4\cdot2^x`

The rule for function g(x) is,

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

The function becomes,

`\begin{gathered} f(x)=4\cdot2^x \\ f(x-2)=4\cdot2^(x-2)=4\cdot(2^x)/(2^2)=2^x \\ f(x-2)+3=2^x+3 \end{gathered}`

Therefore,

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

The graph of the function g(x) is,