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.
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]
41. Domain: [latex]\left(-\infty ,\infty \right)\\[/latex]
43. Domain: [latex]\left(-\infty ,\infty \right)\\[/latex]
45. Domain: [latex]\left(-\infty ,\infty \right)\\[/latex]
47. [latex]\begin{cases}f\left(-3\right)=1;& f\left(-2\right)=0;& f\left(-1\right)=0;& f\left(0\right)=0\end{cases}\\[/latex]
49. [latex]\begin{cases}f\left(-1\right)=-4;& f\left(0\right)=6;& f\left(2\right)=20;& f\left(4\right)=34\end{cases}\\[/latex]
51. [latex]\begin{cases}f\left(-1\right)=-5;& f\left(0\right)=3;& f\left(2\right)=3;& f\left(4\right)=16\end{cases}\\[/latex]
53. Domain: [latex]\left(-\infty ,1\right)\cup \left(1,\infty \right)\\[/latex]
55. Window: [latex]\left[-0.5,-0.1\right][/latex] Range: [latex]\left[4,\text{ }100\right]\\[/latex]
![Graph of the equation from [0.1, 0.5].](https://courses.lumenlearning.com/vccs-mth163-17sp/wp-content/uploads/sites/1621/2015/06/CNX_Precalc_Figure_01_02_222.jpg)
Window: [latex]\left[0.1,\text{ }0.5\right][/latex] Range: [latex]\left[4,\text{ }100\right][/latex]
57. [latex]\left[0,\text{ }8\right]\\[/latex]
59. Many answers. One function is [latex]f\left(x\right)=\frac{1}{\sqrt{x - 2}}\\[/latex].
61. The domain is [latex]\left[0,\text{ }6\right][/latex]; it takes 6 seconds for the projectile to leave the ground and return to the ground.
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- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..
