Determine whether the relation represents a function. If it is a function, state the domain and range. 1)

Transcription

1 MAT 103 TEST 2 REVIEW NAME Determine whether the relation represents a function. If it is a function, state the domain and range. 1) Circle the correct response: Function Not a function Domain: Range: 2) Alice Brad Carl snake cat dog Circle the correct response: Function Not a function Domain: Range: 3) {(19, -4), (3, -3), (3, 0), (12, 3), (28, 5)} Circle the correct response: Function Not a function Domain: Range: 4) {(-4, 20), (-3, 13), (0, 4), (3, 13), (5, 29)} Circle the correct response: Function Not a function Domain: Range: 1

2 Determine the domain of the function. Express answer in interval notation. 5) f(x) = - 5x-8 6) f(x) = x x + 3 Domain: Domain: 7) f(x) = x+ 5 Domain: Provide an appropriate response. 8) A rule that produces a correspondence between two sets of elements such that to each element of the first set there corresponds one and only one element of the second set is called a. 9) In a correspondence between two set, the first set (consisting of the input values) is called the. Find the function value. 10) Find f(9) when f(x) = 4-8x2. 11) Given that f(x) = 5x2-2x, find f(a - 6). Give answer in simplest form. 2

3 The graph of a function f is given. Use the graph to answer the question. 12) Use the graph of f given below to find f(-25) f(-25) = Provide an appropriate response. 13) If g(x) = -4x2 + x - 9, find: a) g(-3) b) g(0) c) g 1 2 Solve the problem. 14) The function F described by F(x) = 2.75x can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose humerus is cm long. Round your answer to the nearest two decimal places. 3

4 15) The point at which a company's costs equals its revenue is the break-even. C represents cost, in dollars, of x units of a product. R represents the revenue, in dollars, for the sale of x units. Find the number of units that must be produced and sold in order to break even. Show work. C(x) = 15x + 12,000 R(x) = 18x ) To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h. W(h) = Choose the appropriate response by circling the letter of your choice. 17) How can the graph of f(x) = - x - 1 be obtained from the graph of y = x? A) Shift it horizontally 1 unit to the right. Reflect it across the x-axis. B) Shift it horizontally -1 unit to the left. Reflect it across the x-axis. C) Shift it horizontally 1 unit to the left. Reflect it across the x-axis. D) Shift it horizontally 1 unit to the left. Reflect it across the y-axis. Choose the appropriate response. 18) How can the graph of f(x) = -(x + 4 )2-6 be obtained from the graph of y = x2? A) Shift it horizontally 4 unit to the right. Reflect it across the y-axis. Shift it 6 units up. B) Shift it horizontally 4 unit to the right. Reflect it across the y-axis. Shift it 6 units down. C) Shift it horizontally 4 unit to the left. Reflect it across the x-axis. Shift it 6 units up. D) Shift it horizontally 4 unit to the left. Reflect it across the x-axis. Shift it 6 units down. 4

5 Provide an appropriate response. 19) The following graph represents the result of applying a sequence of two transformations to the graph of a basic function. Identify the basic (parent) function and describe the transformation(s). Write the equation for the given graph. Equation of parent function: Transformations: Equation for given graph: Write an equation for a function that has a graph with the given transformations. 20) The graph of y = x is shifted 3 units to the left. Then the graph is shifted 9 units upward. Equation of transformed function: 21) The graph of y = x3 is vertically stretched by a factor of 5, and the resulting graph is reflected across the x-axis. Equation of transformed function: 5

6 22) Given the function y = - x-1 +3, a) Write the equation of the parent function: b) List the transformations that the graph of the parent function must undergo to obtain the graph of the given function. c) Sketch the graph of the given function. d) State the domain and range of the given function using interval notation. Domain: Range: Create a table of values and then graph the piecewise function. 23) f(x) = x + 5 if x < 1 3 if x 1 6

7 Answer the following question using algebraic methods. 24) For the parabola with equation f(x) = 4x2-32x + 63, find: a) The equation of the axis of symmetry b) The coordinates of the vertex. Determine whether there is a maximum or minimum value for the given function, and find that value. 25) f(x) = -x2 + 20x -104 Max or min? Value: 26) f(x) = x2 + 18x + 90 Max or min? Value: Find the range of the given function. Express your answer in interval notation. 27) f(x) = 4x2 + 16x + 19 Range: 28) f(x) = -(x + 7)2-2 Range: 7

8 29) Given the function f(x) = x2-3x - 4, complete the followingusing algebraic methods. SHOW ALL WORK. a) Does the parabola open upward or downward? b) Find the equation of the axis of symmetry. c) Find the coordinates of the vertex. d) Find the y-intercept. Write the answer as an ordered pair. e) Find the x-intercepts of the graph, if any. Write the answer(s) as ordered pairs. f) Use your answers from parts a - e to neatly graph the parabola on the axes below. Sketch the axis of symmetry as a dotted line. Label the vertex and the intercepts. 8

9 Write the function. 30) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x) represents the total profit for producing x widgets. a) Given R(x) = 60x x2 and C(x) = 3x + 10, find the equation for P(x). Expess the function in simplest form. b) Graph the profit function on your calculator and determine the number of widgets that must be produced in order to maximize the profit. What is the maximum profit? Round answers to nearest whole number. Use the REGRESSION feature on a graphing calculator. 31) The average retail price in the Spring of 2000 for a used Camaro Z28 coupe depends on the age of the car as shown in the following table. Age, x Price, y 18,325 15,925 13,685 11,805 10, Find the quadratic model that best estimates this data. Round your answer to whole numbers. y = 9

10 32) As the number of farms has decreased in South Carolina, the average size of the remaining farms has grown larger, as shown below. AVERAGE ACREAGE YEAR PER FARM 1900 (x = 0) 1910 (x = 10) Let x represent the number of years since a) Use a graphing calculator to view the scatterplot of the data. b) Use a graphing calculator to fit a quadratic function to the data. Round your answer to five decimal places. y = c) Use your model (regression equation) from part b) to estimate the average acreage per farm in Round to the nearest whole number. d) Should we use this model to predict the acreage per farm in 2009? Explain. 10