Practice Exam II No Calculator Part Problem 1: Graph the following functions A. B.
C.
D. Problem 2: Determine the intercepts, vertex, and axis of symmetry. Then use this information to sketch the graph. Problem 3: Solve the inequality. Problem 4: Consider the polynomial below. A. List the real zeros and multiplicities B. Determine whether the graph crosses or touches the x-axis at each x-intercept. C. Determine the maximum number of turning points on the graph. D. Determine the behavior. That is, find the power function that the graph of f resembles for large values of |x|.
Calculator Part Problem 5: Shown below is the graph of y = f (x). Sketch the graph of y = 1/3 f (-x) - 2.
Problem 6: A rectangle is inscribed in a semicircle of radius 4 as shown below. Let P = (x,y) be the point in the first quadrant that is a vertex of the rectangle and is on the circle.
A. Express the area A of the rectangle as a function of x. B. Express the perimeter p of the rectangle as a function of x. C. For what value of x is A the largest? What is this largest A? D. For what value of x is p the largest? What is the largest p?
Problem 7: The two data sets below represent two different runner's distances (in miles) vs. time (in seconds). For each of them sketch the graph of the scatter diagram. Then determine if a linear model or a quadratic model best describes the graph. Sketch these best fitting curve on the scatter diagram. If it is a line, interpret the slope. Then use your model to predict the times of each for a distance of 6 miles.
Problem 8: The demand equation for selling x liters of fresh carrot juice at a health food store at a price of p dollars is given by x(p) = -6p + 50 A. Find the revenue as a function of p. B. What price should the store sell the juice in order to maximize revenue? C. Use your calculator's graphing capabilities to determine the range prices that produces a revenue greater than $20. |