Honors Pre-Calculus Summer Assignment Name This assignment will be due the first day of class. Late assignments will have ten points deducted for each day late. Show ALL WORK for ALL PROBLEMS. Credit will not be given to those answers lacking written work.
1) The given graph shows the cost of a 30-second television spot (in thousands of dollars) during the Super Bowl from 1989 to 2003. Approximate the percent increase in the cost of a 30-second spot from Super Bowl XXIII in 1989 to Super Bowl XXXV in 2001. 2) A Soccer player passes the ball from a point that is 18 yards from the end-line and 12 yards from the sideline. The pass is received by a teammate who is 42 yards from the same end-line and 50 yards from the same sideline as shown in the figure. a) How long was the pass? b) Find the coordinates of the midpoint of the pass. 3) Use algebraic tests to check for symmetry with respect to both axes and the origin
4) The Pennsylvania State University had enrollments of 40,571 students in 2000 and 41,289 students in 2004 at its main campus in University Park, Pennsylvania. a) Assuming the enrollment growth is linear, find a linear model that gives the enrollment in terms of the years t, where t = 0 corresponds to 2000. b) Use your model from part (a) to predict the enrollment in 2008 and 2010. c) What is the slope of your model? Explain its meaning in the context of the situation. 5) Explain how you could show that the points A (2, 3), B (2, 9), and C(4, 3) are the vertices of a right triangle. 6) Determine whether the equation represents y as a function of x. Explain your reasoning. c) d)
7) Consider the function f(x) = x + 8 + 2. Find the following. a) f( 8) b) f(x + 5) c) f(4x 2 ) 8) Complete the table. 9) Find all real values of x such that f(x) = 0. c) d)
10) Find the domain of each function. 11) Find the difference quotient and simplify your answer. c) d)
12) An open box of maximum volume is made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides. a) The table shows the volume V (in cubic centimeters) of the box for various heights x (in centimeters). Use the table to estimate the maximum volume. b) Plot the point (x, V) from the table in part (a). Does the relation defined by the ordered pairs represent V as a function of x? c) If V is a function of x, write the function and determine its domain with respect to the context of the problem. d) Use a graphing utility to find the maximum volume of the box. Round your answer to three decimal places
13) Use a graphing utility to graph the function. Determine the intervals over which the function is increasing, decreasing, or constant. 14) Use both algebraic and graphical methods to determine whether the function is even, odd, or neither. Explain your reasoning.
15) Find the average rate of change of the function from x 1 to x 2. 16) Write the height h of the rectangle as a function of x. h h 17) If f is an even function, in each case determine whether g is even, odd, or neither. Explain. a) g(x) = f(x) b) g(x) = f( x) c) g(x) = f(x) 2 d) g(x) = f(x 2)
18) Graph the function without a calculator. Explain your solution.
19) Identify the Function c) d) e) f) g) h)
20) Write Equations for the piecewise-defined function. 21) Determine whether the lines L 1 and L 2 passing through the pairs of points are parallel, perpendicular, or neither.
22) Use the graph of f to sketch each graph. c) d) 23) Write an equation for the function that is described by the given characteristics. The shape of f(x) = x 3, but moved six units to the left, four units downward, and reflected over the x-axis.
24) A square concrete foundation is prepared as a base for a cylindrical tank. a) Write the radius r of the tank as a function of the length of x of the sides of the square. b) Write the area A of the circular base of the tank as a function of the radius r. c) Find and interpret (A r)(x). 25) The function given by y = 0.03x 2 + 245.50, 0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit, where x is the percent load for a diesel engine. a) Find the inverse function. Explain what each variable represent in the inverse function. b) Use a graphing utility to graph the inverse function. c) The exhaust temperature of the engine must not exceed 500 degrees Fahrenheit. What is the percent load interval?