Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

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

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

b) $f\left(x\right)\le 0$

Step-by-Step Solution

Answer

a)$(-\infty ,-2)$ or $(2,\infty )$

b) $[-2,2]$

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 $x<-2$ or $x>2$.
• In set builder form, for $f\left(x\right)>0$, $\left\{x|x<-2 or x>2\right\}$. 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 $[-2,2]$.