Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

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

a)$g\left(x\right)<0$ 

b) $g\left(x\right)\ge 0$

Step-by-Step Solution

Answer

a) $(-\infty ,-1)$ or $(4,\infty )$

b) $[-1,4]$

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 $x<-1$ or $x>4$.
• In set builder form, for $g\left(x\right)<0$, $\left\{x\right|x<-1 or x>4\}$. Also, in interval notation it is denoted as $(-\infty ,-1)$ 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 $[-1,4]$.