Question

graph the exponential function.
\\( g(x) = -\frac{3}{2}(2)^x \\)
plot five points on the graph of the function. then click on the graph - a - function button.

Explanation:

Step1: Choose x-values

Let's choose \( x = -2, -1, 0, 1, 2 \) to find corresponding \( y \)-values.

Step2: Calculate for \( x = -2 \)

Substitute \( x = -2 \) into \( g(x)=-\frac{3}{2}(2)^{x} \):
\( g(-2)=-\frac{3}{2}(2)^{-2}=-\frac{3}{2}\times\frac{1}{4}=-\frac{3}{8} \)
So the point is \( (-2, -\frac{3}{8}) \).

Step3: Calculate for \( x = -1 \)

Substitute \( x = -1 \):
\( g(-1)=-\frac{3}{2}(2)^{-1}=-\frac{3}{2}\times\frac{1}{2}=-\frac{3}{4} \)
Point: \( (-1, -\frac{3}{4}) \).

Step4: Calculate for \( x = 0 \)

Substitute \( x = 0 \):
\( g(0)=-\frac{3}{2}(2)^{0}=-\frac{3}{2}\times1 = -\frac{3}{2} \)
Point: \( (0, -\frac{3}{2}) \).

Step5: Calculate for \( x = 1 \)

Substitute \( x = 1 \):
\( g(1)=-\frac{3}{2}(2)^{1}=-\frac{3}{2}\times2=-3 \)
Point: \( (1, -3) \).

Step6: Calculate for \( x = 2 \)

Substitute \( x = 2 \):
\( g(2)=-\frac{3}{2}(2)^{2}=-\frac{3}{2}\times4=-6 \)
Point: \( (2, -6) \).

Answer:

The five points are \( (-2, -\frac{3}{8}) \), \( (-1, -\frac{3}{4}) \), \( (0, -\frac{3}{2}) \), \( (1, -3) \), \( (2, -6) \). These points can be plotted on the graph to sketch \( g(x)=-\frac{3}{2}(2)^{x} \).