Question

I have a graph with the question. If the parent function is y= 2 to the power of x plus 2, which is the function of the graph

Answer 1

The parent function of the graph is

`y=2^x`

The function of the grapg will be

`y=2^{x\text{ + a}}\text{ + b}`

at x equals infinity y equals 1

Therefore

`\begin{gathered} \text{x =}\infty\text{ then y = 1} \\ \text{this implies} \\ b\text{ = 1} \end{gathered}`

Therefore the function will now be

`y=2^{x\text{ + a}}\text{ + 1}`

from the graph

x = 2 when y = 2

Therefore,

`\begin{gathered} 2=2^{2\text{ + a}}\text{ + 1} \\ 2-1=2^{2\text{ + a}} \\ 1=2^{2\text{ + a}} \\ \text{recall 1 = 2}^0 \\ 2^0=2^{2\text{ + a}} \\ 2\text{ + a = 0} \\ a\text{ = - 2} \end{gathered}`

Therefore, the function is

`y=2^{x\text{ - 2}}\text{ + 1}`