1. (10 points) Plot the following points. You can use the www.desmos.com/calculator a. b. c. d. e. f. g. h. A(8,19), B(13,-5), C(-7,-9) What is the length of line segment AB? What is the mid-point of line segment AB? What is the length of line segment BC? What is the mid-point of line segment BC? What is the length of line segment CA? What is the mid-point of line segment CA? Triangle ABC looks like a right triangle. Show mathematically whether it actually is or is not a right triangle. 2. (10 points) Write the equations of the following. a. A line with slope 3 and y-intercept 5. b. A circle of radius 4 centered on the point (5,-3) c. A line with slope -3 which passes through the point (-2,1) 3. (10 points) What type of symmetry do each of the following equations have? (even, odd, or neither). If there is symmetry, what is the equation of the axis of symmetry? Plot each of the equations and the axis of symmetry (or to show that it has no axis of symmetry) to verify your answer. a. y = (x - 5)(x + 5) b. y = x3 - x2 -2x + 1 c. y = x3 - x d. y = x2 -2x + 6 e. y = |2x + 1| 4. (10 points) What is the domain and range of the following functions? Write your answer in interval notation. Use the graphing program www.desmos.com/calculator to verify your answer. a. y = -x2 + 4x - 4 b. y = x4 + 2x3 - 5x2 - 6x c. y = sqrt(x - 4) - 3 d. y = sqrt(x2 - 4) - 3 e. y = sqrt[ 25 - (x+2)2 ] + 3 5. (10 points) Given the following function : y = f(x) = 3x + 2 Make the following shifts and scale changes to get a. y1 = f(x) -2 b. y2 = f(x-2) c. y3 = 2f(x) d. y4 = f(3x) e. y5 = f(x) * f(x) 6. (10 points) Write a new equation which shifts the following equations. Use the graphing program to plot both the original and new equations to verify your answer. a. y = 2x + 5, new equation is shifted 3 units to the right b. y = -4x + 1, new equation is shifted 2 units down c. (x -4)2 + (y + 2)2 = 32, new equation is shifted 2 units to the left and 1 unit up d. y = (x - 1)2 + 2, new equation is shifted1 unit to the right and 3 units up e. y = 2x, new equation is shifted 1 unit to the left and 2 units down 7. (10 points) Let f(x) = x2 and g(x) = x - 2 a. What is f o g(x)? b. What is g o f(x)? c. What is f f(x) ? d. What is g'(x) = [ g(x+h) - g(h)] / h ? e. What is f '(x) = [ f(x+h) - f(x)] / h? 8. (10 points) Given the following function: y = x3 - 4x2 - x -1 for -1 <= x <= 4 a. Plot the function. b. What is the maximum value for y? c. What is the minimum value for y? d. What is the range of y? 9. (20 points) The cost function for making a certain product is C(x) = 3x + 5 per item, where x is the number of items. The selling price per item is p(x) = -x/2 + 10 The revenue received if x items are sold is R(x) = x*p(x) The profit made if x items are sold is Profit(x) = R(x) - C(x) Using the graphing calculator a. b. c. d. e. Plot C(x) Plot R(x) Plot Profit(x) What is number of items that should be made and sold if Profit(x) is a maximum? What is the maximum profit