Solutions to Try Its

1. $\left\{-5,0,5,10,15\right\}$

2. $\left(-\infty ,\infty \right)$

3. $\left(-\infty ,\frac{1}{2}\right)\cup \left(\frac{1}{2},\infty \right)$

4. $\left[-\frac{5}{2},\infty \right)$

5. values that are less than or equal to –2, or values that are greater than or equal to –1 and less than 3;
$\left\{x|x\le -2\text{or}-1\le x<3\right\}$; $\left(-\infty ,-2\right]\cup \left[-1,3\right)$

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 $x$ for $f\left(x\right)=\sqrt[3]{x}$ because you can take the cube root of any real number. So the domain is all real numbers, $\left(-\infty ,\infty \right)$. When dealing with the set of real numbers, you cannot take the square root of negative numbers. So $x$ -values are restricted for $f\left(x\right)=\sqrt[]{x}$ to nonnegative numbers and the domain is $\left[0,\infty \right)$.

5. Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the $x$ -axis and $y$ -axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpoints with an open circle. Use an arrow to indicate $-\infty$ or $\text{ }\infty$. Combine the graphs to find the graph of the piecewise function.

7. $\left(-\infty ,\infty \right)$

9. $\left(-\infty ,3\right]$

11. $\left(-\infty ,\infty \right)$

13. $\left(-\infty ,\infty \right)$

15. $\left(-\infty ,-\frac{1}{2}\right)\cup \left(-\frac{1}{2},\infty \right)$

17. $\left(-\infty ,-11\right)\cup \left(-11,2\right)\cup \left(2,\infty \right)$

19. $\left(-\infty ,-3\right)\cup \left(-3,5\right)\cup \left(5,\infty \right)$

21. $\left(-\infty ,5\right)$

23. $\left[6,\infty \right)$

25. $\left(-\infty ,-9\right)\cup \left(-9,9\right)\cup \left(9,\infty \right)$

27. Domain: $\left(2,8\right]$   Range $\left[6,8\right)$

29. Domain: $\left[-4, 4\right]$   Range: $\left[0, 2\right]$

31. Domain: $\left[-5,\text{ }3\right)$   Range: $\left[0,2\right]$

33. Domain: $\left(-\infty ,1\right]$   Range: $\left[0,\infty \right)$

35. Domain: $\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]$   Range: $\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]$

37. Domain: $\left[-3,\text{ }\infty \right)$   Range: $\left[0,\infty \right)$

39. Domain: $\left(-\infty ,\infty \right)$

41. Domain: $\left(-\infty ,\infty \right)$

43. Domain: $\left(-\infty ,\infty \right)$

45. Domain: $\left(-\infty ,\infty \right)$

47. $\begin{cases}f\left(-3\right)=1;& f\left(-2\right)=0;& f\left(-1\right)=0;& f\left(0\right)=0\end{cases}$

49. $\begin{cases}f\left(-1\right)=-4;& f\left(0\right)=6;& f\left(2\right)=20;& f\left(4\right)=34\end{cases}$

51. $\begin{cases}f\left(-1\right)=-5;& f\left(0\right)=3;& f\left(2\right)=3;& f\left(4\right)=16\end{cases}$

53. Domain: $\left(-\infty ,1\right)\cup \left(1,\infty \right)$

55. Window: $\left[-0.5,-0.1\right]$   Range: $\left[4,\text{ }100\right]$

Window: $\left[0.1,\text{ }0.5\right]$   Range: $\left[4,\text{ }100\right]$

57. $\left[0,\text{ }8\right]$

59. Many answers. One function is $f\left(x\right)=\frac{1}{\sqrt{x - 2}}$.

61. The domain is $\left[0,\text{ }6\right]$; it takes 6 seconds for the projectile to leave the ground and return to the ground.