Solutions
Solutions to Try Its
1. [latex]\left\{-5,0,5,10,15\right\}\\[/latex] 2. [latex]\left(-\infty ,\infty \right)\\[/latex] 3. [latex]\left(-\infty ,\frac{1}{2}\right)\cup \left(\frac{1}{2},\infty \right)\\[/latex] 4. [latex]\left[-\frac{5}{2},\infty \right)\\[/latex] 5. values that are less than or equal to –2, or values that are greater than or equal to –1 and less than 3; [latex]\left\{x|x\le -2\text{or}-1\le x<3\right\}\\[/latex]; [latex-display]\left(-\infty ,-2\right]\cup \left[-1,3\right)\\[/latex-display]6. Domain = [1950, 2002] Range = [47,000,000, 89,000,000]
7. Domain: [latex]\left(-\infty ,2\right]\\[/latex] Range: [latex]\left(-\infty ,0\right]\\[/latex]
8.
![Graph of f(x).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200702/CNX_Precalc_Figure_01_02_0272.jpg)
Solutions for Odd-Numbered Section Exercises
1. The domain of a function depends upon what values of the independent variable make the function undefined or imaginary. 3. There is no restriction on [latex]x[/latex] for [latex]f\left(x\right)=\sqrt[3]{x}\\[/latex] because you can take the cube root of any real number. So the domain is all real numbers, [latex]\left(-\infty ,\infty \right)\\[/latex]. When dealing with the set of real numbers, you cannot take the square root of negative numbers. So [latex]x[/latex] -values are restricted for [latex]f\left(x\right)=\sqrt[]{x}[/latex] to nonnegative numbers and the domain is [latex]\left[0,\infty \right)\\[/latex]. 5. Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the [latex]x[/latex] -axis and [latex]y[/latex] -axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpoints with an open circle. Use an arrow to indicate [latex]-\infty [/latex] or [latex]\text{ }\infty \\[/latex]. Combine the graphs to find the graph of the piecewise function. 7. [latex]\left(-\infty ,\infty \right)\\[/latex] 9. [latex]\left(-\infty ,3\right]\\[/latex] 11. [latex]\left(-\infty ,\infty \right)\\[/latex] 13. [latex]\left(-\infty ,\infty \right)\\[/latex] 15. [latex]\left(-\infty ,-\frac{1}{2}\right)\cup \left(-\frac{1}{2},\infty \right)\\[/latex] 17. [latex]\left(-\infty ,-11\right)\cup \left(-11,2\right)\cup \left(2,\infty \right)\\[/latex] 19. [latex]\left(-\infty ,-3\right)\cup \left(-3,5\right)\cup \left(5,\infty \right)\\[/latex] 21. [latex]\left(-\infty ,5\right)\\[/latex] 23. [latex]\left[6,\infty \right)\\[/latex] 25. [latex]\left(-\infty ,-9\right)\cup \left(-9,9\right)\cup \left(9,\infty \right)\\[/latex] 27. Domain: [latex]\left(2,8\right][/latex] Range [latex]\left[6,8\right)\\[/latex] 29. Domain: [latex]\left[-4, 4\right][/latex] Range: [latex]\left[0, 2\right]\\[/latex] 31. Domain: [latex]\left[-5,\text{ }3\right)[/latex] Range: [latex]\left[0,2\right]\\[/latex] 33. Domain: [latex]\left(-\infty ,1\right][/latex] Range: [latex]\left[0,\infty \right)\\[/latex] 35. Domain: [latex]\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]\\[/latex] Range: [latex]\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]\\[/latex] 37. Domain: [latex]\left[-3,\text{ }\infty \right)\\[/latex] Range: [latex]\left[0,\infty \right)\\[/latex] 39. Domain: [latex]\left(-\infty ,\infty \right)\\[/latex]![Graph of f(x).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200703/CNX_Precalc_Figure_01_02_214.jpg)
![Graph of f(x).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200705/CNX_Precalc_Figure_01_02_216.jpg)
![Graph of f(x).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200706/CNX_Precalc_Figure_01_02_218.jpg)
![Graph of f(x).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200707/CNX_Precalc_Figure_01_02_220.jpg)
![Graph of the equation from [0.1, 0.5].](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200709/CNX_Precalc_Figure_01_02_222.jpg)
![Graph of the equation from [0.1, 0.5].](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25200709/CNX_Precalc_Figure_01_02_222.jpg)