Question

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

a) $f\left(x\right)>0$

b)$f\left(x\right)\le 0$

Short answer

a)$(-\infty ,-2)$or$(2,\infty )$

b)$[-2,2]$

Step-by-step solution

Part (a) Step 1. Given Information

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

Part (a) Step 2. Observe the graph

• From the graph, it is observed that the value of $y$or $f\left(x\right)$is positive for role="math" localid="1646049546322" $x<-2$or $x>2$.
• In set builder form, for $f\left(x\right)>0$, $\left\{x|x<-2orx>2\right\}$. Also, in interval notation it is denoted as$(-\infty ,-2)or(2,\infty )$.

Part (b) Step 1. Given Information

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

Part (b) Step 2. Observe the graph 

• From the graph, it is observed that the value of $y=f\left(x\right)$is negative or equal to 0 for $-2\le x\le 2$.
• In set builder form, for $f\left(x\right)\le 0$, $\left\{x\right|-2\le x\le 2\}$. Also, in interval notation it is denoted as $[-2,2]$.