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Pre-Calculus Midterm Exam Review

Pre-Calculus Midterm Exam Review

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Pre-Calculus Midterm Exam Review

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  1. Pre-Calculus Midterm Exam Review I’m excited!

  2. Is the graph a function or a relation? Function Function Relation

  3. State the domain of the function: All real numbers except 1 or -1 All real numbers except 3 or -3 All real numbers except 5 All real numbers except 0 and 5

  4. Find the composition functions below:

  5. Find the x- and y- intercepts: (12,0) and (0,6) (6,0) and (0,-4)

  6. Find the zero of each function:

  7. Dominic is opening a bank. He determined that he will need $22,000 to buy a building and supplies to start. He expects expenses for each following month to be $12,300. Write an equation that models the total expense y after x months.

  8. Determine whether the graphs of the pair of equations are parallel, coinciding, or neither. x - 2y = 12 and 4x + y = 20 3x - 2y = -6 and 6x - 4y = -12 Neither Coinciding

  9. Write an equation of the line that passes through the points given: (-2,4) and (6,-4) (3,-5) and (0,4)

  10. Write an equation of a line using the information given. 1. No slope, (3,4) 2. slope = 3, (-3, -7) Slope is undefined VERTICAL LINE

  11. How can you tell if two lines are perpendicular? • Their slopes are opposite reciprocals • HOW CAN WE TELL IF THEY ARE PARALLEL? • Their slopes are the SAME

  12. Given f(x) and g(x), find (f/g)(x)

  13. Solve this system of three variables:

  14. Find the product of each: 2X3 2X2 DOES NOT EXIST

  15. Evaluate the determinant of this 3x3 matrix: -4 1 3 -10 0 -2 3 0 -7 1 DOWNHILL - UPHILL (18+280+0) - (0+0-8) (0+56+12) - (0+4-18) 68 – (-14) 82 246+8 254

  16. Evaluate each function given: 1. f(a2) 2. f(3b4)

  17. Graph each function: 1. f(x) = 3x – 4 2. f(x) = -⅔x + 1

  18. Find the values of x and y for which the matrix equation is true. I would use substitution: I would use substitution:

  19. Given the two matrices, perform the following operations. A = B = 1. 3B 2. 2A - C Impossible

  20. Find the inverse of each matrix. 1. 2. Does not exist

  21. Graph each inequality: 1. 2x + y – 3 < 0 2. x + 3y – 6 ≥ 0

  22. Determine the intervals of increasing and decreasing for each function: Decreasing -1.5 < x < 0.2 Increasing x < -1.5, x > 0.2 Decreasing x < 1 Increasing x > 1

  23. What lines are symmetric to each function given: 1. 2. x = 4 y = -2 x = 0 y = 0

  24. Graph each function and it’s inverse. 1. 2. f(x) f(x) f-1(x) f-1(x)

  25. Determine whether the critical pt given is a max, min, or pt of inflection. x = 0 x = 1 1. 2. MAX MIN

  26. Approximate the real zero. 1. 2. Rule of thumb: go from -5 to 5 for your x-values xy -5 -65 -4 -25 -3 -5 -2 1 -1 -1 0 -5 -5 2 5 3 31 xy -5 435 -4 138 -3 19 -2 -6 -1 3 0 10 3 2 -6 3 19 So there is zeroes between -3 and -2, -2 and -1, 1 and 2 So there is zeroes between -3 and -2, -2 and -1, 1 and 2 Or you could just plug each answer and see which one gets you closest to a ZERO If they want a decimal approximation, you need to make another t-chart going by 0.1 in between these approximated zeros.

  27. Solve the system of inequalities by graphing

  28. Use the related function to find the min and max. 1. 2.

  29. Determine the vertical asymptotes of each function VA: x = 0 VA: x = ⅓ VA: x = 4, x = 0

  30. Graph each rational function Hole at x = 0 Hole at x = -2

  31. Find the roots of: A.) B.) C.) 2, -1 D.) -2, 1 USE THE COMMON ROOT AND DO SYNTHETIC DIVISION FIRST 2 IS COMMON AMONG ALL THE ANSWERS AFTER SYNTHETIC DIVISION, TRY TO FACTOR, OR QUADRATIC FORMULA TO FIND THE REST OF THE ROOTS.

  32. Find the number of positive, negative, and imaginary roots possible for this function: 3, 1 positive roots 0 Negative roots Each row adds up to degree of polynomial P N I 0 2 1 0 4 In a polynomial equation, if there is four changes in signs of the coefficients of the terms, __________________________ there is 3 or 1 positive roots

  33. Using Law of Sines In ΔABC if A = 63.17°, b = 18, and a = 17, find B 2. In ΔABC if A = 29.17°, B = 62.3°, and c = 11.5, find a

  34. Determine the type of discontinuity for each function:

  35. Find the maximum value for this system of inequatilites: • Infeasible? Unbounded? Optimal solutions?

  36. Solve this rational inequality: • Use a number line

  37. Find this trig value: 1. Given

  38. Evaluate each problems using the unit circle:

  39. Determine for each function if it is odd, even, or neither? EVEN Odd functions are symmetric with respect to the origin: (a,b) and (-a,-b) Even functions are symmetric with respect to the y-axis: (a,b) and (-a,b) BOTH ORIGIN EVEN

  40. List all possible rational roots of each function: P: 1, 2, 5, 10 Q: 1 P: 1,3 Q: 1, 2, 4

  41. Use the triangles below to find missing cos A, sin A, tan A A 8 ft. 5 ft.

  42. Use the unit circle to find each: 0 undefined -1

  43. State the amplitude for each function: Amplitude = none Amplitude = 2 Amplitude = 1

  44. Find the period for each function: Period = π/k = π Period = 2π/k = 2π/3 or 120° Period = 2π/k = 6π or 1080°

  45. Graph each function VA: x = 5 HA: y = 0 VA: x = -3 HA: y = 0