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Section 8

Polynomial and Rational Inequalities

In Exercises 1β3, the graph of a quadratic function Ζ is given. Use the graph to find the solution set of each equation or inequality. See Example 1.(a) $x^{2}-4 x+3=0$(b) $x^{2}-4 x+3>0$(c) $x^{2}-4 x+3<0$

In Exercises 1β3, the graph of a quadratic function Ζ is given. Use the graph to find the solution set of each equation or inequality. See Example 1.(a) $3 x^{2}+10 x-8=0$(b) $3 x^{2}+10 x-8 \geq 0$(c) $3 x^{2}+10 x-8<0$

The solution set of the inequality $x^{2}+x-12<0$ is the interval $(-4,3) .$ Without actually performing any work, give the solution set of the inequality $x^{2}+x-12 \geq 0$

Solve each inequality, and graph the solution set. $$(x+1)(x-5)>0$$

Solve each inequality, and graph the solution set. $$(x+6)(x-2)>0$$

Solve each inequality, and graph the solution set. $$(x+4)(x-6)<0$$

Solve each inequality, and graph the solution set. $$(x+4)(x-8)<0$$

Solve each inequality, and graph the solution set. $$x^{2}-4 x+3 \geq 0$$

Solve each inequality, and graph the solution set. $$x^{2}-3 x-10 \geq 0$$

Solve each inequality, and graph the solution set. $$10 x^{2}+9 x \geq 9$$

Solve each inequality, and graph the solution set. $$3 x^{2}+10 x \geq 8$$

Solve each inequality, and graph the solution set. $$4 x^{2}-9 \leq 0$$

Solve each inequality, and graph the solution set. $$9 x^{2}-25 \leq 0$$

Solve each inequality, and graph the solution set. $$6 x^{2}+x \geq 1$$

Solve each inequality, and graph the solution set. $$4 x^{2}+7 x \geq-3$$

Solve each inequality, and graph the solution set. $$z^{2}-4 z \geq 0$$

Solve each inequality, and graph the solution set. $$x^{2}+2 x<0$$

Solve each inequality, and graph the solution set. $$3 x^{2}-5 x \leq 0$$

Solve each inequality, and graph the solution set. $$2 z^{2}+3 z>0$$

Solve each inequality, and graph the solution set. $$x^{2}-6 x+6 \geq 0$$

Solve each inequality, and graph the solution set. $$3 x^{2}-6 x+2 \leq 0$$

Solve each inequality. See Example 3.$$(4-3 x)^{2} \geq-2$$

Solve each inequality. See Example 3.$$(7-6 x)^{2} \geq-1$$

$$(3 x+5)^{2} \leq-4$$

Solve each inequality. See Example 3.$$(8 x+5)^{2} \leq-5$$

Solve each inequality, and graph the solution set. See Example 4.$$(x-1)(x-2)(x-4)<0$$

Solve each inequality, and graph the solution set. See Example 4.$$(2 x+1)(3 x-2)(4 x+7)<0$$

Solve each inequality, and graph the solution set. See Example 4.$$(x-4)(2 x+3)(3 x-1) \geq 0$$

Solve each inequality, and graph the solution set. See Example 4.$$(x+2)(4 x-3)(2 x+7) \geq 0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{x-1}{x-4}>0$$

Solve each inequality, and graph the solution set.$$ \frac{x+1}{x-5}>0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{2 x+3}{x-5} \leq 0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{3 x+7}{x-3} \leq 0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{8}{x-2} \geq 2$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{20}{x-1} \geq 1$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{3}{2 x-1}<2$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{6}{x-1}<1$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{x-3}{x+2} \geq 2$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{m+4}{m+5} \geq 2$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{x-8}{x-4}<3$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{2 t-3}{t+1}>4$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{4 k}{2 k-1 } < k$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{r}{r+2}<2 r$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{2 x-3}{x^{2}+1} \geq 0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{9 x-8}{4 x^{2}+25}<0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{(3 x-5)^{2}}{x+2}>0$$

Solve each inequality, and graph the solution set. See Examples 5 and $6 .$$$\frac{(5 x-3)^{2}}{2 x+1} \leq 0$$

Give the domain and the range of each function. See Section 7.3.$$\{(0,1),(1,2),(2,4),(3,8)\}$$

Give the domain and the range of each function. See Section 7.3.$$f(x)=x^{2}$$

Decide whether each graph is that of a function. See Section 7.3