6.2 assignment
question 3 of 7 (1 point) | question attempt: 1 of 2
$g(x)=-\frac{3}{2}(2)^{x}$
plot five points on the graph of the function. then click on the graph-a-function button.

Question

Accepted Answer

# Explanation:
## Step1: Substitute $x = - 2$
Substitute $x=-2$ into $g(x)=-\frac{3}{2}(2)^{x}$.
$$
\begin{align*}
g(-2)&=-\frac{3}{2}(2)^{-2}\
&=-\frac{3}{2}\times\frac{1}{4}\
&=-\frac{3}{8}=- 0.375
\end{align*}
$$
So the point is $(-2,-0.375)$

## Step2: Substitute $x=-1$
Substitute $x = - 1$ into $g(x)=-\frac{3}{2}(2)^{x}$.
$$
\begin{align*}
g(-1)&=-\frac{3}{2}(2)^{-1}\
&=-\frac{3}{2}\times\frac{1}{2}\
&=-\frac{3}{4}=-0.75
\end{align*}
$$
So the point is $(-1,-0.75)$

## Step3: Substitute $x = 0$
Substitute $x = 0$ into $g(x)=-\frac{3}{2}(2)^{x}$.
$$
\begin{align*}
g(0)&=-\frac{3}{2}(2)^{0}\
&=-\frac{3}{2}\times1\
&=-\frac{3}{2}=-1.5
\end{align*}
$$
So the point is $(0,-1.5)$

## Step4: Substitute $x = 1$
Substitute $x = 1$ into $g(x)=-\frac{3}{2}(2)^{x}$.
$$
\begin{align*}
g(1)&=-\frac{3}{2}(2)^{1}\
&=-\frac{3}{2}\times2\
&=-3
\end{align*}
$$
So the point is $(1,-3)$

## Step5: Substitute $x = 2$
Substitute $x = 2$ into $g(x)=-\frac{3}{2}(2)^{x}$.
$$
\begin{align*}
g(2)&=-\frac{3}{2}(2)^{2}\
&=-\frac{3}{2}\times4\
&=-6
\end{align*}
$$
So the point is $(2,-6)$

# Answer:
The five points are $(-2,-0.375)$, $(-1,-0.75)$, $(0,-1.5)$, $(1,-3)$, $(2,-6)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Substitute \(x = - 2\)

Step2: Substitute \(x=-1\)

Step3: Substitute \(x = 0\)

Step4: Substitute \(x = 1\)

Step5: Substitute \(x = 2\)

Answer: