Question

What is the shape of the graph of the function? g(x)= 3/2 (2/3) ^x

Answer 1

Answer:

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

Step-by-step explanation:

Given the function

$g\left(x\right)=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x$

Determining the y-intercept

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

so

substituting x = 0 in the fuction

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x$

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^0$

Apply rule:  $a^0=1,\:a\ne \:0$

$y=1\cdot \frac{3}{2}$

$y=\frac{3}{2}$

$y = 1.5$

Therefore, the point representing the y-intercept is:

• (0, 1.5)

Determining the x-intercept

We know that the value of the x-intercept can be determined by setting y = 0, and determining the corresponding value of x.

so

substituting y = 0 in the function

$0=\frac{3}{2}\left(\frac{2}{3}\right)^x$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$\left(\frac{2}{3}\right)^x=0$

We know that $a^{f\left(x\right)}$ can not be zero or negative for x ∈ R

Thus, NONE represents the x-intercept.

Please check the attached graph.

From the graph, it is clear that option B is the correct option.