Question

In problems 3-6, use the figure to solve each inequality.

a)$g\left(x\right)<0$

b)$g\left(x\right)\ge 0$

Short answer

a)$(-\infty ,-1)$or$(4,\infty )$

b)$[-1,4]$

Step-by-step solution

Part (a) Step 1. Given Information 

It is given that, $g\left(x\right)<0$and the graph is,

Part (a) Step 2. Observe the graph 

• From the graph, it is observed that the value of $y=g\left(x\right)$is negative for localid="1646305079342" $x<-1$or $x>4$.
• In set builder form, for $g\left(x\right)<0$, localid="1646305088829" $\left\{x\right|x<-1orx>4\}$. Also, in interval notation it is denoted as localid="1646305102141" $(-\infty ,-1)$or $(4,\infty )$.

Part (b) Step 1. Given Information  

It is given that, $g\left(x\right)\ge 0$and the graph is,

Part (b) Step 2. Observe the graph  

• From the graph, it is observed that the value of $y=g\left(x\right)$is positive or equal to 0 for $-1\le x\le 4$.
• In set builder form, for $g\left(x\right)\ge 0$, $\left\{x\right|-1\le x\le 4\}$. Also, in interval notation it is denoted as $[-1,4]$.