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Pre-Calculus Midterm Review Packet 1. Describe each graph by stating if it is a relation or function. 2. State the domain of each function: f (x) = 2x +1 x - 3x + 2 2 3. Find (g f )(x) if f (x) = x 2 -1, and g(x) = 3x - 5 4. Find the x- and y-intercept for x – 2y + 5 = 0 5. Find the zero of the function f(x) = -5x + 10 6. Sam is opening his own business. He determined that he will need $3,200 to but supplies to start. He expects expenses for each following month to be $500. Write an equation that models the total expense y after x months. 7. Determine whether the graphs of the pair of equations x + y = 6 and 2x + 3y = 12 are parallel, coinciding, or neither. 8. Write an equation of the line that passes through the points (-1,4) and (5,-2) 9. Write an equation of a line that has no slope and passes through the point (3,-10) 10. How can you tell if two lines are perpendicular? æfö 11. Given f(x) = x2 - x + 3 and g(x) = 2x + 1, find ç ÷(x) è gø 2x + y - z = 3 12. Solve the system of equations by elimination. x+y+z =5 x - 2y + z = 2 é ù é ù 13. If A = ê 0 1 ú and B = ê 2 -1 5 ú , find the product of A and B. ë -1 3 û ë -1 0 3 û 14. Find the value of 3 -1 0 1 5 1 4 0 -1 . 15. Find the f(3a3) for f(x) = 2x2 – 5x 16. Find the zero of the function f(x) = -2x – 3, then graph the function. 17. Find the values of x and y for which the matrix equation is true. éë 2x é ù 18. Given B = ê 0 1 2 ú , C = ë -1 -1 0 û é2 1 3ù ê ú ê-4 0 -2 ú Find 2B – C êë 5 2 1 úû y ùû = éë y -1 x + 5 ùû é ù 19. Find the inverse of ê 1 2 ú . ë -5 3 û 20. Graph the inequality 4x + y - 3 > 0? 21. Determine the intervals on which the function f(x) = x3 - x2 + 2x is increasing and the intervals on which the function is decreasing. (x -1)2 (y + 3)2 22. For which line(s) is the graph of + =1 is symmetric? 4 1 23. Which is the graph of f(x) = x2 - 3 and its inverse? 24. Determine whether the given critical point of x = -5 is the location of a relative maximum, relative 1 minimum, or a point of inflection for the function f (x) = x 2 + 5x +1 2 25. Approximate the real zero(s) of f (x) = x 3 - 2x 2 + 5x - 5 to the nearest tenth. 26. Solve the system of inequalities by graphing. x-y ≤2 3x - y < 1 y ≥0 27. Sean has $10,000 to deposit in two different savings accounts. He wants at least $4,000 in the account with 5% interest. He wants no less than $6,000 in the account with 4% interest. For the equation l(x,y) = 30x + 70y find the maximum interest if the vertices are (3,5), (3,7), and (5,5). 28. Determine the equation of the vertical asymptote for the function f (x) = 29. Graph the function f (x) = x-2 3(x -1) x 2 -1 x -1 30. Find the roots of x 3 + 3x - 4 = 0 31. In a polynomial equation, if there are two changes in sign of the coefficients of the terms, _______. 32. In if A = 53°, B = 72°, and b = 15, find a to the nearest tenth. ì x 2 + 3 x >1 f (x) = í î2x x £1 B. point discontinuity D. infinite discontinuity 33. Determine the type of discontinuity this function exhibits. A. jump discontinuity C. none of these 34. Find the maximum value of f(x, y) = 2x + y - 4 for the system of inequalities: y ≤ ⅓x + 1 y ≤ 2x - 1 x≥0 y≥0 A. Unbounded C. 1 35. Solve B. alternate Optimal solutions D. Infeasible x > 0. x -4 2 36. If sin q = 3 find csc θ 5 37. Evaluate tan 7p 3 38. Which is an odd function? A. y = x B. x 2 + y 2 =1 C. y = x 3 39. List the possible rational roots of 5x 3 + 5x 2 - 2x + 2 = 0 P 40. Find cos P. 8 cm 2 cm D. y = x 2 41. Use the unit circle to find sec (-270°) . 5 42. State the amplitude for the function y = - cosq 3 æq p ö 43. Find the period of the function y = sec ç - ÷ è2 4 ø 44. Use the parent graph f(x) = 1 1 to graph the function g(x) = + 4. x x-3