Question

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

Answer 1

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:

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