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Study Guides > MATH 1314: College Algebra

Solutions

Solutions to Try Its

1. {5,0,5,10,15}\left\{-5,0,5,10,15\right\}\\ 2. (,)\left(-\infty ,\infty \right)\\ 3. (,12)(12,)\left(-\infty ,\frac{1}{2}\right)\cup \left(\frac{1}{2},\infty \right)\\ 4. [52,)\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; {xx2or1x<3}\left\{x|x\le -2\text{or}-1\le x<3\right\}\\; (,2][1,3)\left(-\infty ,-2\right]\cup \left[-1,3\right)\\
6. Domain = [1950, 2002]   Range = [47,000,000, 89,000,000]
7. Domain: (,2]\left(-\infty ,2\right]\\   Range: (,0]\left(-\infty ,0\right]\\
8.
Graph of f(x).
 

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 xx for f(x)=x3f\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 xx -values are restricted for f(x)=xf\left(x\right)=\sqrt[]{x} to nonnegative numbers and the domain is [0,)\left[0,\infty \right)\\. 5. Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the xx -axis and yy -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. (,3]\left(-\infty ,3\right]\\ 11. (,)\left(-\infty ,\infty \right)\\ 13. (,)\left(-\infty ,\infty \right)\\ 15. (,12)(12,)\left(-\infty ,-\frac{1}{2}\right)\cup \left(-\frac{1}{2},\infty \right)\\ 17. (,11)(11,2)(2,)\left(-\infty ,-11\right)\cup \left(-11,2\right)\cup \left(2,\infty \right)\\ 19. (,3)(3,5)(5,)\left(-\infty ,-3\right)\cup \left(-3,5\right)\cup \left(5,\infty \right)\\ 21. (,5)\left(-\infty ,5\right)\\ 23. [6,)\left[6,\infty \right)\\ 25. (,9)(9,9)(9,)\left(-\infty ,-9\right)\cup \left(-9,9\right)\cup \left(9,\infty \right)\\ 27. Domain: (2,8]\left(2,8\right]   Range [6,8)\left[6,8\right)\\ 29. Domain: [4,4]\left[-4, 4\right]   Range: [0,2]\left[0, 2\right]\\ 31. Domain: [5, 3)\left[-5,\text{ }3\right)   Range: [0,2]\left[0,2\right]\\ 33. Domain: (,1]\left(-\infty ,1\right]   Range: [0,)\left[0,\infty \right)\\ 35. Domain: [6,16][16,6]\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]\\   Range: [6,16][16,6]\left[-6,-\frac{1}{6}\right]\cup \left[\frac{1}{6},6\right]\\ 37. Domain: [3, )\left[-3,\text{ }\infty \right)\\   Range: [0,)\left[0,\infty \right)\\ 39. Domain: (,)\left(-\infty ,\infty \right)\\ Graph of f(x). 41. Domain: (,)\left(-\infty ,\infty \right)\\ Graph of f(x). 43. Domain: (,)\left(-\infty ,\infty \right)\\ Graph of f(x). 45. Domain: (,)\left(-\infty ,\infty \right)\\ Graph of f(x). 47. {f(3)=1;f(2)=0;f(1)=0;f(0)=0\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. {f(1)=4;f(0)=6;f(2)=20;f(4)=34\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. {f(1)=5;f(0)=3;f(2)=3;f(4)=16\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: (,1)(1,)\left(-\infty ,1\right)\cup \left(1,\infty \right)\\ 55. Window: [0.5,0.1]\left[-0.5,-0.1\right]   Range: [4, 100]\left[4,\text{ }100\right]\\ Graph of the equation from [0.1, 0.5]. Window: [0.1, 0.5]\left[0.1,\text{ }0.5\right]   Range: [4, 100]\left[4,\text{ }100\right] Graph of the equation from [0.1, 0.5]. 57. [0, 8]\left[0,\text{ }8\right]\\ 59. Many answers. One function is f(x)=1x2f\left(x\right)=\frac{1}{\sqrt{x - 2}}\\. 61. The domain is [0, 6]\left[0,\text{ }6\right]; it takes 6 seconds for the projectile to leave the ground and return to the ground.

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