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Jeopardy Math Review Unit 1: Functions and Their Graphs Unit 2: Polynomial and Rational Functions Unit 3: Exponential and Logarithmic Functions Unit 4: Trigonometry Unit 1: Functions and Their Graphs II 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 Final Jeopardy Calculate the midpoint between the points: (8, -5) and (-2, 3) Calculate the distance between the points: (-7, 4) and (1, 6) Midpoint = (3, -1) Distance = root68 = 8.25 Calculate the slope of the line through the given points: Line A: (2, 4) (-3, 5) Slope = -1/5 Line B: (0, -7) (1, -2) Slope = 5 What kind of lines are A and B? perpendicular Write the slope-intercept equation of the line that meets the following criteria: Line C: Parallel to the line y = 3x – 9 and through the point (2, -2) y = 3x - 8 Given the following pairs of points, write the point-slope form of the line: Line F: (1, 2) and (0, -5) y - 2= 1/7(x – 1) OR y + 5 = 1/7(x – 0) f-1(x) = x2 – 8 3 vertex = (-2, 6) axis of symmetry: X = -2 x-intercept(s) = -5 and 1 y-intercept(s) = 4 max @ (-2, 6) max/min = equation of graph: y = -(x + 2)2 + 6 Write the equation of the quadratic function given the vertex and point. Vertex = (4, 5) Point = (3, 2) y = -3(x – 4)2 + 5 Completely factor the polynomials: -2x(x + 2)(x -1) (3x - 1)(x + 2) Use Synthetic Division to find the quotient. x2 -2x +6 Write the complex number in standard form and write its conjugate. 15 + 6i 15 – 6i Find the sum. Find the product. 18 – 3i -27 + 23i Write the complex fraction in standard form. -2 + 29i 13 Solve the nonlinear inequality: -2 < x < 7 Evaluate the exponential function: f(2/3) = 0 Write the logarithm as an exponential: 361/2 = 6 Solve the equation for x: x=5 Evaluate the logarithms: -3 -3 1 Write the exponential as a logarithm: log5(25) = 2 Solve the logarithmic equation for x: x = -3 Using a calculator, evaluate the logarithm: 1.44 Expand the logarithmic equation: = log(4y3 +2) – 6log(x) – 2 log(z) Condense the logarithmic equation: = log8[(z-5)2/(x+3)6] Solve for x. x = 32 x = 6.77 x = 100.86 Convert the radian measure to degrees: 330° Convert the degree measure to radians: 5π/6 Find the supplement of the angle: 7π/4 Find the complement of the angle: π/4 Evaluate the following: Undefined Root2/2 -root3/2 Find the values of x. x = root65 = 8.06 x=7 Evaluate the trigonometric functions of the angle. 5/root61 -6/root61 -5/6 -root10/10 -root10 3root10/10 root10/3 -1/3 -3 f(2) = 11 x = -1, 1 f(x + 3) = 5x2 + 30x + 36 x = all real numbers except -7 x = all real numbers greater than or equal to -12 f(x) is neither Use bracket notation to describe all increasing, decreasing, or constant intervals of the graph. INC DEC (-∞, -8] [-8, -5] INC [-5, 8) DEC (8, 6] INC [6, ∞) Write the equation of the quadratic parent function with A = -1, B = 5 and C = -3. y = -(x+5)2 – 3 Describe the effects that each value (A, B, and C) has on the graph of the quadratic parent function. A = -1 means the graph is flipped over the x-axis B = 5 means the graph is shifted to the left 5 units C = -3 means the graph is shifted down 3 units f(x) + g(x) = x2 +x +1 f(x)•g(x) = 3x3 - 7x2 + 8x -2 f(g(x)) = 9x2 - 12x + 5 Unit 5: Graphs and Inverses of Trigonometric Functions Fill in the table and write the equation that the graph models. amplitude = 3 period = π left endpoint = (0, 5) max = 5 a= 3 b= 2 c= 0 d= 2 y = 2 + 3cos(2x)