Stewart - Calculus 8e ET Chapter Form A If , find Solve each equation for x (a) (b) Simplify the expression Fill in the blanks Let , where Determine whether f is even, odd, or neither Find the range of the function © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A The graphs of and are given a) For what values of is ? and b) Find the values of A spherical balloon with radius inches has volume Find a function that represents the amount of air required to inflate the balloon from a radius of inches to a radius of inches It makes sense that the larger the area of a region, the larger the number of species that inhabit the region Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in of the caves by the equation (a) The cave called mission impossible near puebla, mexico, has suface area of How many species of bats would expect to find in that cave? (b) If you discover that species of bats live in cave estimate the area of the cave © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 10 The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function Complete the table and find the slope 11 Plot the graph of the function in (a) the standard viewing window and (b) the indicated window f (x) = x , [-3, 3] [-5, 5] 12 Plot the graph of the function f in an appropriate viewing window f (x) = 2x – 5x + 4x + 27 13 Find the points of intersection of the graphs of the functions Express your answers accurate to five decimal places = 0.3 – 1.1x – 3.5; = –0.2 + 0.4x + 6.9 14 Determine whether f is one-to-one y x © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 15 If f (x) = find f (–4), f (0), and f (1) 16 Refer to the graph of the function f in the following figure y f ( x) –4 –3 –2 –1 –1 x –2 –3 –4 –5 a Find f (3) b Find the value of x for which (i) c Find the domain and range of f and 17 Let 18 Find and (ii) Find if 19 Let and 20 Find the function such that Find and © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A Answer Key , even a) –2, 10 b) , a) b) 10 species ; slope = © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 11 a y 10 –10 10 x x x –10 b y –3 –5 y 12 140 120 100 80 60 40 20 –4 –3 –2 –1 –20 13 (–3.30104, 3.40021), (6.30104, 1.47979) © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 14 Yes 15 f (–4) = 19, f (0) = 3, f (1) = 16 a b (i) (ii) 3, c D: [3, 6], R: [–3, 1] 37 17 18 19 –6 20 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form B Find all solutions of the equation correct to two decimal places Solve each equation for x (a) (b) Find the exact value of the expression Find the range of the function Express the function in the form of Plot the graph of the function f in an appropriate viewing window f (x) = 5x – 3x + 3x – x + 26 Find the points of intersection of the graphs of the functions Express your answers accurate to five decimal places = 0.3 – 1.2x – 3.4; = –0.2 + 0.2x + 6.3 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form B Determine whether f is one-to-one y x The graph of f is given Sketch the graph of on the same set of axes y 0.5 y = f ( x) 0.5 x 10 Find the inverse of f Then sketch the graphs of f and f(x) = on the same set of axes , 11 If f (x) = find f (–1), f (0), and f (1) © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form B 12 Refer to the graph of the function f in the following figure y f (x) –4 –3 –2 –1 –1 x –2 –3 –4 –5 a Find f (0) b Find the value of x for which (i) c Find the domain and range of f and (ii) 13 Determine whether the function is even, odd, or neither 14 The following figure shows a portion of the graph of a function f defined on the interval Sketch the complete graph of f if it is known f is odd y –1 x –1 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G Find (a) for the function f and the real number a Select the correct answer ; a b c d –2 –1 Find the exact value of the given expression sin–1 Use the laws of logarithms to expand the expression ln Simplify the expression Select the correct answer a b c d 10 If 25 32 10 , evaluate the difference quotient 11 A rectangle has perimeter m Express the area of the rectangle as a function of one of its sides Select the correct answer of the length a b c d e © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G 12 Find the domain of the function 13 The graph shown gives the weight of a certain person as a function of age Find the age at which the person started an exercise program Select the correct answer a b c d e 20 35 54 38 14 An open rectangular box with volume has a square base Express the surface area of the box as a function of the length of a side of the base 15 Determine whether f is even, odd, or neither Select the correct answer a neither b even c odd 16 Find the range of the function 17 If and , find a function g such that © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G 18 The graph of the function follows Choose the graph of y –9 –6 –3 x –3 –6 –9 a c y –9 –6 y 9 6 3 –3 x –9 –6 –3 –3 –3 –6 –6 –9 –9 x d b y y 9 6 –9 –6 –3 3 x –9 –6 –3 –3 –3 –6 –6 –9 –9 x © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G 19 Suppose that the graph of is given f is given Describe how the graph of the function can be obtained from the graph of f Select the correct answer a b c d e Shift the graph units to the right and units down Shift the graph units to the right and units up Shift the graph units to the left and units up Shift the graph units to the left and units down None of these 20 Which of the following graphs is the graph of the function? Graph –2 –1 Graph –4 –3 –2 –1 4 Graph –4 –3 –2 –1 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G Answer Key y –4 –3 –2 –1 x 0.3 x –1 y 0.3 –0.3 –0.3 D B B ln (x + 4) – 10 11 12 13 A none of these C D ln (x – 5) © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form G 14 15 16 17 18 19 20 B C A Graph © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H Plot the graph of the function f in an appropriate viewing window Find the points of intersection of the graphs of the functions Express your answers accurate to five decimal places Select the correct answer f (x) = 0.5 – 1.8 + 2.2x – 4; = 2.8x – 4.3 a (–0.55126, –5.84352), (3.87001, 6.53604) b (–0.55126, –1.54352) (0.28124, 10.83604) (3.87001, 0.78748) c (–0.55126, –1.54352) (3.87001, 0.78748) d (–0.55126, –5.84352), (0.28124, –3.51252) (3.87001, 6.53604) The function is graphed below y 15 12.5 10 7.5 2.5 –10 –7.5 –5 –2.5 –2.5 2.5 7.5 10 x –5 –7.5 –10 Find the inverse function of © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H Determine whether the function is one-to-one a Yes b No Find the exact value of the given expression tan–1 Use the laws of logarithms to expand the expression ln Simplify the expression Select the correct answer a b c d 18 216 729 Solve the equation 10 A box with an open top is to be constructed from a rectangular piece of card board with dimensions in by in by cutting out equal squares of side at each corner and then folding up the sides as in the figure Express the volume of the box as a function of © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H 11 Find an expression for the function whose graph is the bottom half of the parabola Select the correct answer a b c d e 12 Find the domain of the function 13 Find the domain and sketch the graph of the function What is its range? f (x) = 14 The graph shown gives the weight of a certain person as a function of age Find the age at which the person started an exercise program Select the correct answer a b c d e 20 54 38 35 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H 15 Find the domain Select the correct answer a b c d e 16 Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H follows Choose the graph of 17 The graph of the function y –5 –4 –3 –2 –1 –1 x –2 –3 –4 –5 a c y y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 x –5 –4 –3 –2 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 y b d 4 3 2 1 x 2 3 x y –5 –4 –3 –2 –1–1 –5 –4 –3 –2 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 x © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H 18 Sketch the graph of 19 Find the function over one period and its domain if and 20 The graph of the function has been stretched horizontally by a factor of Find the function for the transformed graph Select the correct answer a b c d © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H Answer Key y –4 –3 –2 –1 x –1 D B ln (x + 5) – ln (x – 6) C x = ln –5 10 11 A 12 (– 13 D: (– , ); R: (– , ) © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H y –2 –1 –1 x x 14 D 15 D y 16 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 17 A 18 y –2 –1 –1 x –2 –3 –4 –5 © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form H 19 20 C © 2016 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ...Stewart - Calculus 8e ET Chapter Form A The graphs of and are given a) For what values of is ? and b) Find the... duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 10 The relationship between the Fahrenheit and Celsius temperature scales... duplicated, or posted to a publicly accessible website, in whole or in part. Stewart - Calculus 8e ET Chapter Form A 15 If f (x) = find f (–4), f (0), and f (1) 16 Refer to the graph of the