MAT135 Review for Final Exam Dugopolski 1 1. Find the slope of the line passing through the points ( 1, 7) and (5,4). A. 211 B. 116 C. 34 D. 611 2. Factor completely: 338 32x y xy. A. 2 (2 4 )(2 4 )xy x y x y B. 8 ( 2 )( 2 )xy x y x y C. 2 5 3 32 (4 16 )x x y x y D. (4 4 )(2 4 )xy x y x y 3. Identify the x- and y-intercepts of the graph of the equation3 3 7xy. A. x-intercept: 3,07 y-intercept: 30,7 B. x-intercept: 7,03 y-intercept: 70,3 C. x-intercept: 7,03 y-intercept: 70,3 D. x-intercept: 3,07 y-intercept: 30,7 4. Solve: 5 2 3 8xx. A. The equation has no solution. B. 3x C. 54x D. 8x 5. Find a set of ordered pairsx y, bgthat represents y as a function of x. A. 5, 3 , 3,5 , 1,1 B. 5, 3, 9,1 C. 5, 3 , 3, 9 , 5,1 D. 5, 3 , 9,1 , 9,5 , 1, 9MAT135 Review for Final Exam Dugopolski 2 6. Estimate the slope of the line. You may assume that each tick mark represents one unit. A. 1 B. 1 C. 27 D. 72 7. What is the vertex of 2( ) 2 ?f x x x A. (1,1) B. (1, 1) C. ( 1,1) D. ( 1, 1) 8. Solve: 24 20 25rr. A. 525,4rr B. 4525,4rr C. 52r D. 52r 9. Simplify: 815 93a b. A. 3 33 2ab a B. 3 33 9 23a b a C. 3 333ab ab D. 3 33 23ab a 10. Simplify: 3222.5xx A. 121258x B. 128125x C. 12125x D. 8x y xMAT135 Review for Final Exam Dugopolski 3 11. What is true of the graph below? You may assume that each tick mark represents one unit. A. The y-intercept is at( 2,0). B. The graph has a negative slope. C. (0) 5f. D. The graph passes through the point( 1, 3). 12. Find the solution to the equation 66435xx. A. 24x B. 6x C. 22x D. 4x 13. Solve: 22 4 1 0.xx A. 222x B. 222x C. 12x D. 12x 14. Which of the following is the graph of 2()f x x shifted two units to the left and three units down? A. 2( ) ( 2) 3f x x B. 2( ) ( 3) 2f x x C. 2( ) ( 2) 3f x x D. 2( ) ( 3) 2f x x x yMAT135 Review for Final Exam Dugopolski 4 15. Find the slope-intercept form of the equation of the line through the point (2,7) parallel to the line 9 4 1xy. A. 9245yx C. 9542yx B. 4295yx D. 9542yx 16. Perform the indicated operation: ( 3 2 )( 3 7 )ii. A. 5 27i B. 23 15i C. 5 15i D. 23 15i 17. Write an equation of the line passing through the point (6, 10) with an undefined slope. A. 6x B. 10x C. 6y D. 10y 18. If2( ) 2 3 and ( ) 1 5f x x x g x x, for what values are( ) ( )f x g x? A. 13x B. 13x C. 132x D. 132x 19. Which of the following graphs is symmetric about the y-axis? A. ( ) 2f x x C. 2( ) 3 1f x x x B. 2( ) 2f x x D. ( ) 4f x x 20. What is the range of the function shown below? You may assume that each tick mark represents one unit. A. ( , ) B. [4, ) C. ( ,4] D. [ 2,2] y xMAT135 Review for Final Exam Dugopolski 5 21. Factor completely5 4 3 214 28 35a a b a b. A. 3 2 2(14 28 35 )a a ab b B. 4 3 2 27 (2 4 5 )a a a b a b C. 5 2 4 27 (2 4 5 )a a a b a b D. 3 2 27 (2 4 5 )a a ab b 22. If6()2xf x xx, for what values of x is f(x) =8? A. 0x B. 4, 4xx C. 16x D. 8, 2xx 23. A salesperson earns $30,000 a year plus 8% commission on his total sales. Write an equation that expresses this relationship between his earnings (E) and total sales (S). A. 30,000 8ES B. 30,000 8ES C. 8 -30,000ES D. 30,000 0.08ES 24. Solve: 6 3 9x. A. 1,2 B. 1,2 C. , 1 2, D. , 1 2, 25. The graph below represents a company’s profit from selling tickets for a weekend trip. The x-axis represents the number of tickets sold and the y-axis represents the profit made. What is the least number of tickets that must be sold to make a profit of $4,000.00? Please note the scale on the axes. A. 10 B. 20 C. 30 D. 40 x y 1000 2000 3000 4000MAT135 Review for Final Exam Dugopolski 6 26. Solve A mx bx for x. A. Axmb B. x A m b C. Axmb D. Axmb 27. If32( ) 4 6 28f x x x x, evaluate( 2)f. A. 38 B. 36 C. 26 D. 8 28. What is the domain of 26( ) ?( 1)xrxxx A. All real numbers 0, 1xx. B. All real numbers 1x. C. All real numbers 0.x D. All real numbers. 29. What number must be added to 243tt to complete the square? A. 169 B. 49 C. 23 D. 83 30. Simplify: 3216. A. 64i B. 344 C. 64i D. 64 31. If2274( ) , ( )11 18 3 54f x g xx x x x, find( ) ( )f x g x. A. 211 65 306( 2)( 9)( 6)xxx x x B. 211 36( 2)( 9)( 6)xx x x C. 11 34( 2)( 9)( 6)xx x x D. 211 65 18( 2)( 9)( 6)xxx x xMAT135 Review for Final Exam Dugopolski 7 32. What is true of 25 10()7xxfx? A. It is not a polynomial function. B. It is a polynomial function of degree two. C. It is not defined for all real numbers. D. It has no real roots. 33. Factor 324 33 68 15x x x given that 3x is a factor. A. ( 3)( 5)(4 1)x x x C. ( 3)( 5)(4 1)x x x B. ( 3)( 5)(4 1)x x x D. ( 3)( 5)(4 1)x x x 34. If9()1xfxx, find all values for which3()2fx. A. 215x B. x =21 C. x = 15 D. 2x 35. Solve the following system: 5 2 114 7 2xyxy. A. This system of equations has no solution.31 1B. ,15 3C. This system of equations has an infinite number of solutions.D. 3, 2xyxy 36. What is not true of the graph of ()y f x shown below? A. It has three distinct roots. B. ( 4)fis negative. C. It does not cross the x-axis at 0.x D. The domain is,. x yMAT135 Review for Final Exam Dugopolski 8 37. Solve: 66 3 147x. A. 161 119,66 B. 102 119,76 C. 161 30,67 D. 119 35,66 38. 2 3 3 2(8 10 14) (4 9 7 11)y y …