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Q. 3

Expert-verifiedFound in: Page 171

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

b) $[-2,2]$

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

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

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

- 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 $[-2,2]$.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

x | $y=f\left(x\right)$ |

-2 | $\frac{1}{4}$ |

-1 | $\frac{1}{2}$ |

0 | 1 |

1 | 2 |

2 | 4 |

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