Question

Based on the information given in the following graph of a power function, can you determinethe equation of the power function? Why or why not? If you can, find the equation of the powerfunction. If not, describe the equation of the power function as much as you can.

Answer 1

SOLUTIONS

To determine the equation of the power function? Why or why not? If you can, find the equation of the power

`\begin{gathered} (4,2) \\ x=4,y=2 \end{gathered}`

It is easy to get the graph of the exponential function since x - value = 4 and y - value = 2.

An exponential function is defined by the formula f(x) = x^a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The general equation of an exponential function is

`y=x^a`
`\begin{gathered} y=2,x=4 \\ 2=4^a \\ 4^{(1)/(2)}=4^a \\ a=(1)/(2) \end{gathered}`

`y=x^{(1)/(2)}`