SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. x )

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1 Midterm Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the arrow diagram defines a function. 1) Domain Range 1) Determine whether or not the relationship shown in the table is a function. 2) x y ) Does the table define x as a function of y? Find the domain of the function. 3) y = 7x - 6 3) 4) y = -7 x - 4 4) 5) The cost of a rental car for the weekend is given by the function C(x) = x, where x is the number of miles driven. Find and interpret the C-intercept of the graph of this function. 5) 6) It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = 0.22t + 1, for t > 10. Find and interpret f(40). Round your answer to the nearest whole number. 6) Write the equation of the line with the given conditions. 7) passing through (-4, 1) and perpendicular to the line with equation 8x + 7y = -39 7) 8) passing through (5, 5) and parallel to the line with equation 5x + y = 4 8) Find the average rate of change for the function over the given interval. 9) y = x2 + 2x between x = 4 and x = 8 9) 10) y = 7x3 + 5x2-4 between x = 4 and x = 6 10) 11) Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $3500 in 1982 and $61,000 in Let x = 0 represent Find the equation giving yearly sales y. 11) 1

2 12) An electrician charges a fee of $55 plus $40 per hour. Let y be the cost in dollars of using the electrician for x hours. Find the slope-intercept form of the equation. 12) Solve the equation. 13) 5x = - 4x ) 14) 1 5 (r + 6) = 1 (r + 8) 14) 7 Solve the formula for the specified variable. 15) S = 2 rh + 2 r2 for h 15) 16) I = ne nr + R for n 16) Write the best-fit linear model for the data. 17) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Find a linear function that predicts a student's current GPA as a function of his or her entering GPA. 17) Entering GPA Current GPA ) The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Find a linear function that predicts a student's score as a function of the number of hours he or she studied. Hours Score ) 19) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Find a linear function that predicts the number of products sold as a function of the cost of advertising. Cost Number ) 2

3 Does the system have a unique solution, no solution, or many solutions? 20) 2x + 3y = 6 4x + 6y = 12 20) 21) 4x - 16y = 12 y = 1 4 x Solve the system of equations, if a solution exists. 22) -6x + 5y = -34-2x + 2y = ) Does the system have a unique solution, no solution, or many solutions? 23) 6x - y = 22 x + 3y = 10 23) 24) A certain product has supply and demand functions given by p = 7q + 26 and p = 257-4q, respectively, where p is the price in dollars and q is the quantity supplied or demanded at price p. What price gives market equilibrium? 24) Provide an appropriate response. 25) Write the equation of the quadratic function whose graph is shown. 25) 26) A projectile is thrown upward so that its distance above the ground after t sec is given by h(t) = -15t t. After how many seconds does it reach its maximum height? 26) Use factoring to solve the equation. 27) 15y2 + 31y + 10 = 0 27) Solve the equation by completing the square. 28) q2 + 8q - 5 = 0 28) 3

4 29) A certain product has supply and demand functions given by p = 7q + 23 and p = 308-8q, respectively, where p is the price in dollars and q is the quantity supplied or demanded at price p. How many units are supplied and demanded at market equilibrium? 29) Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. 30) x2-5x = 1 30) 31) 10y2 + 23y + 12 = 0 31) 32) A ball is thrown downward from a window in a tall building. The distance traveled by the ball in t seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 235 feet? 32) 33) The function defined by D t = 13t2-73t gives the distance in feet that a car going approximately 50 mph will skid in t seconds. Find the time it would take for the car to skid 304 ft. Round to the nearest tenth. 33) Graph the function. 34) f(x) = -3, if x x, if x < 1 34) 35) f(x) = 8x + 3, if x < 0 4x2-3, if x 0 35) 4

5 Find the requested value. 36) x - 6, if x < 4 f(0) for f(x) = 3 - x, if x 4 36) 37) f(-2) for f(x) = x2 + 5x + 6, if x -2 x, if x > -2 37) Determine if the function is increasing or decreasing over the interval indicated. 38) y = -3x3 ; x < 0 38) 39) y = 2x2 ; x > 0 39) 40) y = -7x4 ; x < 0 40) Solve the equation. 41) x + 8 = x2 + 8x 41) 42) x = x2 + 6x 42) Find a quadratic function that best fits the data. Give answers to the nearest hundredth. 43) x y ) Find a power function that models the data in the table. Round to three decimal places if necessary. 44) x y ) Fill in each blank with the appropriate response. 45) The graph of y = -6(x - 4)2 + 7 can be obtained from the graph of y = x2 by shifting horizontally units to the, vertically stretching by a factor of, reflecting across the -axis, and shifting vertically units in the direction. 45) Find the specified domain and express it in interval notation. 46) For f(x) = 2x - 5 and g(x) = x + 5, what is the domain of f (x)? 46) g 47) For f(x) = x - 2 and g(x) = 1, what is the domain of g/f? 47) x - 9 Find the requested composition of functions. 48) Given f(x) = 4x2 + 6x + 4 and g(x) = 6x - 3, find (g f)(x). 48) 5

6 49) Given f(x) = 8x + 5 and g(x) = 5x - 1, find (f g)(x). 49) 50) Acme Communication finds that the total revenue function associated with producing a new type of cellular phone is R(x) = 209x - x2, and the total cost function is C(x) = x, where x represents the number of units of cellular phones produced. Find the total profit function, P(x). 51) Let C(x) = x be the cost to manufacture x items. Find the average cost per item to produce 40 items. 50) 51) 52) AAA Technology finds that the total revenue function associated with producing a new type of computer chip is R(x) = x2, and the total cost function is C(x) = 2x + 17, where x represents the number of units of chips produced. Find the total profit function, P(x). 53) The function f(x) = 60x computes the number of minutes in x hours. The function g(x) = 24x computes the number of hours in x days. What is (f g)(x) and what does it compute? 52) 53) Verify whether or not the functions are inverses of each other. 54) f(x) = 5x + 25, g(x) = 1 5 x ) Decide whether or not the functions are inverses of each other. 55) f(x) = 1 5x + 1, g(x) = x + 5 x 55) Find the inverse of the function. 56) f(x) = 2x2-7, x 0 56) 57) f(x) = 3 x ) Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. 58) f(x) = x ) 6

7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 59) 2x x = 0 59) A) x = 40.5 B) x = ±10 C) x = 9 D) x = ±9 Solve. 60) 3 3x + 4 = -2 60) A) x = - 4 B) x = -12 C) x = 4 3 D) x = 4 Solve the inequality. 61) x2-4x ) A) x 6 B) -2 x 6 C) x -2 or x 6 D) x -2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The graphs of two functions f(x) and g(x) are given. 62) Solve f(x) g(x). 62) 63) The height h of a ball thrown is given by h(x) = 2x x2, where x is the horizontal distance traveled and both measurements are in feet. At what horizontal distances will the height of the ball be more than 9 ft? (Round distances to the nearest tenth of a foot, if necessary.) 63) 7