<p> MATH 0310 Review for Final Exam</p><p>1. For the graph: y  a. state the coordinates of the  1a ______y- intercept   x 1b______</p><p> b. state the slope           1c______c. write the equation of the </p><p> line  1d______</p><p> d. find the domain 1e______</p><p> e. find the range</p><p>2. Find the slope of the line parallel to the line passing through (3,- 1) and (4,2) . 2.______</p><p>3. State the slope of the line perpendicular to the line 2x- 5 y = 8. 3.______</p><p>2 5 2 5 8 A. - B. - C. D. E. - 5 2 5 2 5</p><p>4. For the following graph of f , y  determine:   4a______a. f 1  x b. the domain of f          4b______ c. the range of f   4c______</p><p></p><p>Revised: May 2010 Page 1 0949715cc17a2251f9ff0544cbe73692.doc 5. Find a linear function whose graph has m = 3 and y -intercept (0,2) . Then graph. y </p><p> </p><p> x</p><p>         </p><p> </p><p></p><p> 5______</p><p>6. A table of values is given. Write the equation of the line through the given points.6______</p><p> x y  2  8 1  3 0 2 1 7 2 12</p><p>7. Determine whether each relation is a function. Answer yes or no. 7______y y y   </p><p>       x   x x                                          8. a. Graph x  3 y y  2 y  b. Graph </p><p> </p><p> </p><p>  x x</p><p>                   </p><p> </p><p> </p><p> </p><p> </p><p>Revised: May 2010 Page 2 0949715cc17a2251f9ff0544cbe73692.doc 9. In 1990, the life expectancy of females was 78.8 yr. In 2000, it was 79.8 yr. Let E(t) represent the life expectancy of females and t the number of years since 1990.</p><p> a. Find a linear function that fits the data. 9a______</p><p> b. Use the function to estimate the life expectancy of females in 2010. 9b______</p><p>10. Find an equation of the line perpendicular to the line x  4y  3 and containing the point (-2, - 4) . Write the equation in the slope-intercept form. 10______</p><p>2 2x - 1 11. Subtract: - 11______x+1 x2 - 1 1- 2x -3 1- 2x A. B. C. x2 -1 (x- 1)( x + 1) x( x - 1)</p><p>-1 4x - 1 D. E. (x- 1)( x + 1) (x+ 1)( x - 1)</p><p> x 18 3 12. Solve: = - 12.______x+4x2 +2 x - 8 x - 2</p><p>13. A biker can travel 18 mph with no wind. The same rider can bicycle 8 miles against the wind in the same time it takes to bicycle 12 miles with the wind. What is the speed of the wind? 13.______</p><p>A. 9 mph B. 3.6 mph C. none of these</p><p>D. 90 mph E. 9 mph</p><p>Revised: May 2010 Page 3 0949715cc17a2251f9ff0544cbe73692.doc For problems 14 – 18, find the following, given that f x  3x  6 and gx  x 2 1 14. g  f x 14______</p><p>15.  f  g2 15______</p><p>16. (f g )( x ) 16.______</p><p>17. domain of gx 17______</p><p>A. (-ゥ, ) B. (-1,1) C. (-1, ) D. {0} E. (- ,1)</p><p> g  18. domain of  x 18______ f </p><p>Solve the system of equations by graphing . y </p><p>2x  3y  6   19______19..  2  y   x  2    3 x           </p><p></p><p></p><p> Solve the following systems of equations. 5y 12  x 20.  20______2x 10y  5</p><p>4x  3y  1 21.  21______3x  5y  13</p><p>22. Write the systems of equations. Then solve. Retail orders. The St. Andrew’s Community Barbecue served 175 dinners. A child’s plate cost $3.50 and an adult plate cost $7.00. A total of $875 was collected. How many of each type of plate were sold? 22. equations: ______</p><p>22. solutions: ______</p><p>Revised: May 2010 Page 4 0949715cc17a2251f9ff0544cbe73692.doc 23. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 200-lb mixture that is 11.8% protein?</p><p>23. equations: ______</p><p>23. solutions: ______</p><p>For the following exercises, solve and graph the solution set on a number line. Then write the solution set in interval notation.</p><p>24. -7�x 2 < 4 24______</p><p>25. 3x  15 or x -1 4 25______</p><p>26. 3x  15 and x -1 4 26______</p><p>27. Let f( x )= 5 - 2 x . Find:</p><p> a. f (–10) 27a______</p><p> b. f (0) 27b______</p><p> c. f (3) 27c______</p><p> d. State the domain of f 27d______</p><p>28. Let f x  3 x</p><p> a. find f  8 28a______</p><p> b. find the domain of f x 28b______</p><p>Simplify.</p><p>29. 3  27x 6 y 8 29______</p><p>A. -9x2 y 2 3 y 2 B. -3x2 y 2 C. -3x3 y 5 D. -3x2 y 2 3 y 2 E. -3x3 y 4</p><p>4x10 30 30______9</p><p>31. 18 31______</p><p>Revised: May 2010 Page 5 0949715cc17a2251f9ff0544cbe73692.doc Perform the indicated operation and simplify.</p><p>32 7x 8x  2x 50x 32______</p><p>33. a. 9  4i– 1 6i 33a______b. 9  4i 1 6i 33b______34. a. Rewrite 6 x 5 with rational exponents. 34a______1 b. Rewrite x 2 in radical notation. 34b______</p><p>35. Rationalize each denominator: x a. 35a______3</p><p>4 b. 35b______3  2</p><p>7 c. 35c______3  i</p><p>Solve #36 and 37.</p><p>36. x = 5x 11 1 36 ______</p><p>37. 3 3x 1  4 37______</p><p>38. Find the distance between the points (-5,7) and (3,1) . 38______</p><p>39. Find the midpoint of the line segment that joins the points (-5,7) and (3,1) . 39______</p><p>40. Find the equation of the circle in standard form if (-5,7) is the center and(3,1) is a point on the circle. 40______</p><p>41. For x  22 +y  62  9 , state the center and radius of the circle. 41______</p><p>Revised: May 2010 Page 6 0949715cc17a2251f9ff0544cbe73692.doc Solve 42 -- 46.</p><p>42. x 2  3x 18  0 42______</p><p>43. x  32  49 43______</p><p>44. x 2  4x  4 44______</p><p>45. 2x 2  2x  5  0 45______</p><p>1 3 A. 1 � 3i B. 2, - 1 C. i D. 1 � 11 i E. 1 � 11 2 2</p><p>46. x 4  5x 2  6  0 46______</p><p>47. Solve f( x )= 3 x2 - 5 x + 1 using a calculator. Round to three decimal places. 47______</p><p>48. The area of a rectangular football field is 90 feet. If the length exceeds the width by one foot, what is the length of the field? 48______</p><p>2 y 49. For f( x) = - x +2 x + 3 find the:  49a.______a. vertex   49b______b. axis of symmetry  x </p><p>         49c______c. direction the parabola opens </p><p> 49d______d. y - intercept   49e______e. x - intercepts </p><p>49f.______f. minimum or maximum value </p><p> g. Graph the function.</p><p>50. Graph the solution set of the system of inequalities. y </p><p> y  x 1   3x  2y  6   x</p><p>         </p><p></p><p></p><p></p><p></p><p>Revised: May 2010 Page 7 0949715cc17a2251f9ff0544cbe73692.doc 8b.</p><p>1. a. (0, 1) d. (-ゥ, )  1  MATH b. m =  e. (-ゥ, )  3  0310 1 Review c. y =  x 1          3  **Answer   Key*   9. a. ( t ) = 0.1t + 78.8 2. m = 3 E b. 80.8 years 5 10. y  4x  4 3. B m = - 2 11 D 4. a. 1 12. x = -3 b.{x x � 4} or [-4, ) 13. B c.{y y 1} or [1, ) 14. g  f x  x 2  3x  7 5. f( x )= 3 x + 2 15. 5</p><p>  16. 3x3- 6 x 2 + 3 x - 6   17. A (-ゥ, )             </p><p>6. y=5 x + 2 18. x x  2 or (-∞, 2)U (2, ∞) 7. Yes; No; Yes</p><p>8a.</p><p> 19. x, y2x  3y  6   20. No solution  21 (4, –5)             </p><p>C  A  175 5 22.  34a. 3.5C  7A  875 x 6 100 children's plates; 75 adults’ plates b. x</p><p>3x x  y  200 35a. 23.  3 .16x  .09y  .118(200) 12  4 2 21 7 80 lbs of soybean meal b. c. + i Revised: 120 May lbs 2010of corn meal Page 8 7 10 10 0949715cc17a2251f9ff0544cbe73692.doc</p><p>) -5-5 65</p>