Question

State the equations and use the graph to determine where the 2 points intersect

Answer 1

Step-by-step explanation:

We are given an exponential function as shown below;

`f(x)=2^x`

When shifted one unit right we have the following;

`m(x)=2^(x-1)`

We also are given the quadratic function;

`g(x)=x^2`

When shifted one unit right and one unit up, we would have;

`n(x)=(x-1)^2+1`

The equations for both functions after the transformations would be;

`\begin{gathered} m(x)=2^(x-1) \\ n(x)=(x-1)^2+1 \end{gathered}`

The graphs of both equations is now shown below;

The two points where m(x) and n(x) intersect are;

`(1,1)\text{ and }(2,2)`

ANSWER:

`\begin{gathered} (a)\text{ }m(x)=2^(x-1) \\ n(x)=(x-1)^2+1 \\ (b)\text{ }(1,1),(2,2) \end{gathered}`