Question

100 PTS PLEASE ANSWER ASAP! <3

Answer 1

$\\ \rm\Rrightarrow g(x)=6(\dfrac{3}{2})^x$

$\\ \rm\Rrightarrow g(-1)=6(\dfrac{3}{2})^{-1}=6(\dfrac{2}{3})=2(2)=4$

$\\ \rm\Rrightarrow g(0)=6$

$\\ \rm\Rrightarrow g(1)=6(\dfrac{3}{2})=3(3)=9$

$\\ \rm\Rrightarrow g(2)=6\times\dfrac{9}{4}=13.2$

Attached the graph

Answer 2

Answer:

Given function:

$g(x)=6\left(\dfrac{3}{2}\right)^x$

To find each of the points, substitute the given values of x into the function:

$x=-1 \implies g(-1)=6\left(\dfrac{3}{2}\right)^{-1}=4$

$x=0 \implies g(0)=6\left(\dfrac{3}{2}\right)^{0}=6$

$x=1 \implies g(1)=6\left(\dfrac{3}{2}\right)^{1}=9$

$x=2 \implies g(2)=6\left(\dfrac{3}{2}\right)^{2}=13.5$

Therefore:

$\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & -1 & 0 & 1 & 2 \\\cline{1-5} g(x) & 4 & 6 & 9 & 13.5 \\\cline{1-5} \end{array}$

As the function is exponential, there is a horizontal asymptote at $y=0$.

Therefore, as $x$ approaches -∞ the curve approaches $y=0$ but never crosses it.

So the end behaviors of the graph are:

• $\textsf{As }x \rightarrow - \infty, \:\:g(x) \rightarrow 0$

• $\textsf{As }x \rightarrow \infty, \:\:g(x) \rightarrow \infty$

Plot the points on the graph and draw a curve through them.