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Test Bank for Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

Test Bank for Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th Edition is your go-to resource for exam questions, providing key insights to boost your score.

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    Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use point - by - point plotting to sketch the graph of the equation. 1) y = x + 5 1) A) B) C) D) 1

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    2) y = x 2 + 1 2) A) B) C) D) 2

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    Determine whether the graph is the graph of a function. 3) 3) A) function B) not a function Determine whether the function is linear, constant, or neither 4) y = x + 3 7 4) A) Linear B) Constant C) Neither Use point - by - point plotting to sketch the graph of the equation. 5) f(x) = 2x x + 2 5) A) B) 3

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    C) D) The graph of a function f is given. Use the graph to answer the question. 6) Use the graph of f given below to find f( - 50 ). 50 - 50 50 - 50 6) A) 80 B) 0 C) - 50 D) 30 Find the function value. 7) Find f( - 6 ) when f(x) = 9 - 3 x 2 . 7) A) 117 B) - 99 C) 27 D) 45 Determine the domain of the function. 8) f(x) = - 7x + 9 8) A) No solution B) All real numbers C) x K 9 7 D) All real numbers except 9 7 Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. 9) x - y 2 = 9 9) A) A function with domain [ B) Not a function; for example, when x = 10, y = ± 1 4

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    Solve the problem. 10) The function F described by F(x) = 2.75x + 71.48 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 30.93 cm long. Round your answer to the nearest four decimal places. 10) A) 43.3000 cm B) 156.5375 cm C) 105.1600 cm D) 13.5775 cm Give the domain and range of the function. 11) f(x) = x 2 + 2 11) A) Domain: all real numbers; Range: [ 2 , Q ) B) Domain: [ 2 , Q ); Range: all real numbers C) Domain: [0 , Q ); Range: [0, Q ) D) Domain: all real numbers; Range: [ 3 , Q ) Provide an appropriate response. 12) How can the graph of f(x) = - x + 1 be obtained from the graph of y = x ? 12) A) Shift it horizontally 1 units to the left. Reflect it across the y - axis. B) Shift it horizontally - 1 units to the left. Reflect it across the x - axis. C) Shift it horizontally 1 units to the left. Reflect it across the x - axis. D) Shift it horizontally 1 units to the right. Reflect it across the x - axis. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) The following graph represents the result of applying a sequence of transformations to the graph of a basic function. Identify the basic function and describe the transformation(s). Write the equation for the given graph. 13) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. 5

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    14) f(x) = x - 2 if x < 1 - 3 if x L 1 14) A) B) C) D) Solve the problem. 15) A retail chain sells washing machines. The retail price p(x) (in dollars) and the weekly demand x for a particular model are related by the function p(x) = 625 - 5 x , where 50 K x K 500. (i) Describe how the graph of the function p can be obtained from the graph of one of the six basic functions: y = x, y = x 2 , y = x 3 , y = x , y = 3 x , or y = x . (ii) Sketch a graph of function p using part (i) as an aid. 15) 6

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    A) (i) The graph of the basic function y = x is vertically expanded by a factor of 625, and shifted up 5 units. (ii) B) (i) The graph of the basic function y = x is reflected in the x - axis and vertically expanded by a factor of 5. (ii) 7

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    C) (i) The graph of the basic function y = x is vertically expanded by a factor of 5, and shifted up 625 units. (ii) D) (i) The graph of the basic function y = x is reflected in the x - axis, vertically expanded by a factor of 5, and shifted up 625 units. (ii) Graph the linear equation and determine its slope, if it exists. 16) 3x + 5y = 11 16) 8

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    A) slope: 3 4 B) slope: 3 4 C) slope: - 3 4 D) slope: - 3 4 Find the slope and y intercept of the graph of the equation. 17) y = 3 x - 4 17) A) Slope = - 4 , y intercept = 3 B) Slope = 3 , y intercept = 4 C) Slope = 3 , y intercept = - 4 D) Slope = 4 , y intercept = 3 9

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    Provide an appropriate response. 18) Use the graph to find the slope - intercept form of the equation of the line. 18) A) y = - x + 3 B) y = x + 3 C) y = x - 3 D) y = 3x For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 19) f(x) = (x + 1 ) 2 - 4 19) A) (A) x - intercepts: - 3 , 1 ; y - intercept: - 3 (B) Vertex ( 1 , - 4 ) (C) Minimum: - 4 (D) y L - 4 B) (A) x - intercepts: - 3 , 1 ; y - intercept: - 3 (B) Vertex ( - 1 , - 4 ) (C) Maximum: - 4 (D) y K - 4 C) (A) x - intercepts: - 3 , 1 ; y - intercept: - 3 (B) Vertex ( - 1 , - 4 ) (C) Minimum: - 4 (D) y L - 4 D) (A) x - intercepts: - 1 , 3 ; y - intercept: - 3 (B) Vertex ( - 1 , - 4 ) (C) Minimum: - 4 (D) y L - 4 Find the slope of the line containing the given points. 20) ( 2 , - 4 ); ( - 5 , 8 ) 20) A) - 7 12 B) 7 12 C) 12 7 D) - 12 7 Use interval notation to write the solution set of the inequality. 21) 3 x + 5 < 29 21) A) ( - Q , 8 ) B) ( 8 , Q ) C) ( - Q , 8 ] D) [ 8 , Q ) 10

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    Provide an appropriate response. 22) Use the graph to find the slope, x - intercept and y - intercept of the line. 22) A) slope = - 1 x - intercept = ( - 7, 0) y - intercept = (0, 7) B) slope = 1 x - intercept = (0, 7) y - intercept = ( - 7, 0) C) slope = - 1 x - intercept = (7, 0) y - intercept = (0, - 7) D) slope = 1 x - intercept = (7, 0) y - intercept = (0, - 7) Solve graphically to two decimal places using a graphing calculator. 23) 1.3 x 2 - 2.1 x - 3.2 > 0 23) A) x < - 0.96 or x > 2.57 B) x < - 2.57 or x > 0.96 C) - 2.57 < x < 0.96 D) - 0.96 < x < 2.57 Solve the problem. 24) The cost of manufacturing a computer part is related to the quantity produced, x, during a production run. When 100 parts are produced, the cost is $300. When 600 parts are produced, the cost is $ 4800 . Find an equation of the line relating quantity produced to cost. Write the final answer in the form C = mx + b. 24) A) C = 9x - 600 B) C = 9x C) C = 9x + 600 D) C = 600x + 9 For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. 25) y = 4 x + 1 25) A) (i) 1 (ii) 1 4 (iii) 1 B) (i) 1 (ii) - 1 4 (iii) 1 C) (i) 1 (ii) - 4 (iii) 4 D) (i) 1 (ii) 1 (iii) 1 4 11

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    The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? 26) 26) A) (i) 2 (ii) Negative B) (i) 3 (ii) Positive C) (i) 2 (ii) Positive D) (i) 3 (ii) Negative Provide an appropriate response. 27) What is the maximum number of x intercepts that a polynomial of degree 2 can have? 27) A) 1 B) 3 C) 2 D) Not enough information is given. For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). 28) f(x) = x + 2 x + 1 28) 12

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    A) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except - 1 (iii) Vertical asymptote: x = - 1; horizontal asymptote: y = 1 (iv) B) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 1 (iii) Vertical asymptote: x = 1; horizontal asymptote: y = 1 (iv) C) (i) x intercept: 2; y intercept: 2 (ii) Domain: all real numbers except 1 (iii) Vertical asymptote: x = 1; horizontal asymptote: y = 1 (iv) 13

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    D) (i) x intercept: - 2; y intercept: 2 (ii) Domain: all real numbers except - 1 (iii) Vertical asymptote: x = - 1; horizontal asymptote: y = 1 (iv) Find the equation of any horizontal asymptote. 29) f(x) = 8 x 2 - 7 x - 2 5 x 2 - 2 x + 9 29) A) y = 0 B) y = 7 2 C) y = 8 5 D) None Write an equation for the lowest - degree polynomial function with the graph and intercepts shown in the figure. 30) 30) A) f(x) = x 2 + 5 x - 6 B) f(x) = x 2 - 6 x + 5 C) f(x) = x 2 + 5 x + 6 D) f(x) = x 2 + 6 x + 5 Solve the problem. 31) Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = x 2 + 4x + 1800. The average cost per unit at a production level of x ovens per day is C (x) = C(x)/x. (i) Find the rational function C . (ii) Sketch a graph of C (x) for 10 K x K 125. (iii) For what daily production level (to the nearest integer) is the average cost per unit at a minimum, and what is the minimum average cost per oven (to the nearest cent)? HINT: Refer to the sketch in part (ii) and evaluate C (x) at appropriate integer values until a minimum value is found. 31) 14

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    A) (i) C (x) = x 2 + 4x + 1800 x (ii) (iii) 44 units; $185.61 per oven B) (i) C (x) = x 2 + 4x + 1800 x (ii) (iii) 22 units; $48.93 per oven C) (i) C (x) = x 2 + 4x + 1800 x (ii) (iii) 42 units; $88.86 per oven D) (i) C (x) = x 2 + 4x + 1800 x (ii) (iii) 61 units; $133.29 per oven Graph the function. 15

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