Exercises 8.5 Practice Problems
1.
Write each of the following in interval notation (Note: you may find it helpful to draw a number line):
\(\displaystyle x \ge -5\)
\(x \le -3\) or \(x \gt 6\)
\(\displaystyle x \neq 88\)
\(x \ge -2\) and \(x \lt 6\)
Everything except \(\pm 6\)
\(\displaystyle x \lt 18\)
Everything except \(0\)
\(x \lt -5\) or \(x \gt -5\)
\(\displaystyle [-5, \infty)\)
\(\displaystyle (-\infty,-3]\cup(6,\infty)\)
\(\displaystyle (-\infty,88)\cup(88,\infty)\)
\(\displaystyle [-2, 6)\)
\(\displaystyle (-\infty,-6)\cup(-6,6)\cup(6,\infty)\)
\(\displaystyle (-\infty,18)\)
\(\displaystyle (-\infty,0)\cup(0,\infty)\)
\(\displaystyle (-\infty, -5)\cup(-5, \infty)\)
2.
Find the domain of the function in the graph below:\([1,3)\)
3.
Find the domain of the function in the graph below:\([1,4)\cup(4,6]\)
4.
Find the domain of the function in the graph below:\([1,9)\)
5.
Find the domain of the function in the graph below:\([-3,1)\cup[2,4]\)
6.
Find the domain of the function in the graph below:\([-1,6]\)
7.
Find the domain of the function in the graph below:\([-2,0]\cup(1,3)\cup[5,7]\)
8.
Find the domain of the function in the graph below:\([-2,0]\cup(2,5)\)
9.
Find the domain of the function in the graph below:\([-1,2)\cup(2,5]\)
10.
Find the range of the function in the graph below:\([0,4)\)
11.
Find the range of the function in the graph below:\([0,9)\)
12.
Find the range of the function in the graph below:\([-1,7)\)
13.
Find the range of the function in the graph below:\([0,9]\)
14.
Find the range of the function in the graph below:\([0,1]\cup(2,7]\)
15.
Find the range of the function in the graph below:\([-2,0]\cup(1,3)\cup[5,7]\)
16.
Find the range of the function in the graph below:\([4,14)\)
17.
Find the range of the function in the graph below:\([-4,2)\cup(2,8]\)
18.
Find the domain of \(f(x)=5x^2-\frac{7x}{2}+\sqrt{29}\text{.}\)\((-\infty, \infty)\)
19.
Find the domain of \(f(x)=\frac{3x^2}{2x-1}\text{.}\)\((-\infty, \frac{1}{2})\cup(\frac{1}{2},\infty)\)
20.
Find the domain of \(f(x)=\sqrt{4x-3}\text{.}\)\([\frac{3}{4}, \infty)\)
21.
Find the domain of \(f(x)=\frac{4x^3}{\sqrt{3x}}\text{.}\)\((0, \infty)\)
22.
Find the domain of \(g(x)=7x^2-\frac{7x}{\sqrt{7}}+\sqrt{31}\text{.}\)\((-\infty, \infty)\)
23.
Find the domain of \(h(x)=15x^6-\frac{19x}{x^2-1}\text{.}\)\((-\infty,-1)\cup(-1,1)\cup(1,\infty)\)
24.
Find the domain of \(f(x)=\frac{\sqrt{2x+3}}{4}\text{.}\)\([-\frac{3}{2}, \infty)\)
25.
Find the domain of \(g(x)=\frac{1}{\sqrt{6x+4}}\text{.}\)\((-\frac{2}{3}, \infty)\)
26.
Find the domain of \(f(x)=13x^{12}-\frac{\pi x}{11}+\sqrt{10}\text{.}\)\((-\infty, \infty)\)
27.
Find the domain of \(f(x)=\frac{x-3}{12x+18}\text{.}\)\((-\infty, -\frac{3}{2})\cup(-\frac{3}{2}, \infty)\)