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Name Date: Algebra 2 & Trigonometry Midterm Review Sheet #4 YOU MUST SHOW ALL WORK, EVEN ON MULTIPLE CHOICE QUESTIONS, IF YOU WANT TO EARN FULL CREDIT! 1. Solve for x: x2 – 36 > 0 x2 – 1 2. Solve for x: 3x + 4 < 0 x–5 3. Solve for x using the quadratic formula: 2x2 - 9x + 2 = 0 4. Solve for x by completing the square: x2 + 9x – 7 = 0 5. Solve for x: x4 – 18x2 + 81 = 0 6. Solve for x: 2x3 + 14x2 – 10x = 0 7. State if the relation is a function, explain your answer. {(7, -2), (4, -2), (1, 3), (0, 9), (4, -1), (2, 9)} 8. Solve for x: 2 x 6 x 1 3 9. Given f(x) = 3x – 8, g(x) = a. f(-9) b. g(12) c. h(-1) d. g(f(6)) e. h(f(g(4))) f. f(g(x)) g. h(f(x)) x 5 and h(x) = x2 – 5x + 1, find: 2 10. Sketch each equation (without using a calculator). State the domain and range of each equation, then state whether the equation a function. a. y = 4x – 9 b. y = x2 – 8x + 3 c. x2 + y2 = 1 e. y= x7 11. Write the inverse of each of the following functions: d. y = -|x| + 5 f. f(x) = 2x + 2 a. f(x)= -8x + 1 12. Using the composition of functions, prove b. g(x) = x3 + 7 f ( x) x2 2 and g ( x ) are inverse x x 1 functions. 13. Given f(x) = x2, write the equation that would shift the graph of the equation 2 units to the right. 14. Given g(x) = |x|, write the equation that would shift the graph of the equation 3 units to the left and 2 units down. 15. Consider the graph of the function f(x) shown: On the same set of axes, sketch the graph of the function f(-x). 16. The graph of the function below represents f(x). On the axes to the right, sketch the graph of the function g(x) = f(x – 3) + 2 17. Simplify. 5 – 7i 3 + 8i 18. Simplify. 4i23 + 8i67 – 3i100 + 2i45 19. Given A = -4 + 7i and B = 2 + -9i, graph A, B and A + B on the grid provided.