Question

(a) Graph$g\left(x\right)=3^x-9$ g

(b) Find the zero of g.

(c) Based on the graph, solve$g\left(x\right)<0$

Short answer

a) The graph of the function is

b) The zero of the function is $x=2$

c)$g\left(x\right)<0$when$x<2$

Step-by-step solution

Step !: Given information

We are given a function$g\left(x\right)=3^x-9$

We create a table

We get

x	$g\left(x\right)=3^x-9$
-1	$-\frac{28}{3}$
0	-8
1	-6
2	0
3	18

The graph of the function can be given as

Part b) Step 2: Solve for g(x)=0

We get,

$$\begin{gathered} g\left(x\right)=0 \\ {3}^x-9=0 \\ {3}^x=9 \\ {3}^x=3^2 \\ x=2 \end{gathered}$$

The zero of the function is at$x=2$

Part c) Step 1: Solve for g(x)<0

As the zero of the function is at x=2

Hence$g\left(x\right)<0$when$x<2$