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Q. 3

Expert-verified
Found in: Page 171

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In problems 3-6, use the figure to solve each inequality.a) $f\left(x\right)>0$b) $f\left(x\right)\le 0$

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

b) $\left[-2,2\right]$

See the 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 $\left(-\infty ,-2\right)or\left(2,\infty \right)$.

## 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 $f\left(x\right)\le 0$, $\left\{x|-2\le x\le 2\right\}$. Also, in interval notation it is denoted as $\left[-2,2\right]$.