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Essential Calculus: Early Transcendentals 2nd Edition Test Bank

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    Stewart_Essential Calc_2ET ch01sec01 MULTIPLE CHOICE 1. The graph of the function is given. State the value of . a. b. c. d. e. ANS: E PTS: 1 DIF: Medium REF: 1.1.3b MSC: Bimodal NOT: Section 1.1 2. The graphs of and are given. For what values of x is ? a. 4, 2

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    b. c. 0 d. e. – 4, 12 ANS: E PTS: 1 DIF: Medium REF: 1.1.4b MSC: Bimodal NOT: Section 1.1 3. 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. a. 35 b. 38 c. 20 d. 54 e. ANS: E PTS: 1 DIF: Medium REF: 1.1.9 MSC: Bimodal NOT: Section 1.1 4. If , find and simplify , where . a. b. c. d. ANS: A PTS: 1 DIF: Easy REF: 1.1.21 MSC: Bimodal NOT: Section 1.1 5. If , evaluate the difference quotient . a. h b. c. d. e. none of these ANS: E PTS: 1 DIF: Medium REF: 1.1.22 MSC: Bimodal NOT: Section 1.1

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    6. Find the domain of the function. a. ( –  , 0)  (0,  ) b. ( –  , 0) c. d. ANS: A PTS: 1 DIF: Easy REF: 1.1.25 MSC: Bimodal NOT: Section 1.1 7. Find the domain and sketch the graph of the function. What is its range? f ( x ) = a. D : ( – , ); R : [0, ) 1 2 3 4 5 6 7 8 9 10 x 1 2 3 4 5 6 7 8 9 10 y c. D : ( – , ); R : ( – , 3] 1 2 3 4 5 6 7 8 –1 –2 x 1 2 3 4 5 6 7 8 9 –1 y b. D : ( – , ); R : ( – , 0] (3, ) d. D : ( – , ); R : [ – 1, )

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    1 2 3 4 5 6 7 8 9 –1 x 1 2 3 4 –1 –2 –3 –4 –5 –6 y 1 2 3 4 5 6 7 8 –1 –2 x 1 2 3 4 5 6 7 8 9 –1 y ANS: C PTS: 1 DIF: Medium REF: 1.1.39 MSC: Bimodal NOT: Section 1.1 8. Find an expression for the function whose graph is the bottom half of the parabola . a. b. c. d. e. ANS: C PTS: 1 DIF: Medium REF: 1.1.45 MSC: Bimodal NOT: Section 1.1 9. A rectangle has perimeter m. Express the area of the rectangle as a function of the length of one of its sides. a. b. c. d. e. ANS: E PTS: 1 DIF: Medium REF: 1.1.47 MSC: Bimodal NOT: Section 1.1 10. 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.

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    a. b. c. d. e. ANS: D PTS: 1 DIF: Medium REF: 1.1.51 MSC: Bimodal NOT: Section 1.1 11. Determine whether the function whose graph is given is even, odd, or neither. 2 4 6 8 10 –2 –4 –6 –8 –10 x 2 4 6 8 10 –2 –4 –6 –8 –10 y a. Even b. Neither c. Odd ANS: A PTS: 1 DIF: Medium REF: 1.1.55 MSC: Bimodal NOT: Section 1.1 12. If the point is on the graph of an even function, what other point must also be on the graph? a. b. c. d. e. None of these

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    ANS: A PTS: 1 DIF: Medium REF: 1.1.57a MSC: Bimodal NOT: Section 1.1 13. Which of the following graphs is neither even nor odd? a. b. c. ANS: C PTS: 1 DIF: Medium REF: 1.1.60 MSC: Bimodal NOT: Section 1.1 NUMERIC RESPONSE 1. The graphs of and are given. Find the values of and . ANS: , PTS: 1 DIF: Medium REF: 1.1.4a MSC: Numerical Response NOT: Section 1.1 2. Find the domain of the function. ANS: PTS: 1 DIF: Medium REF: 1.1.26

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    MSC: Numerical Response NOT: Section 1.1 3. Find the domain of the function. ANS: PTS: 1 DIF: Medium REF: 1.1.27 MSC: Numerical Response NOT: Section 1.1 4. Determine whether f is even, odd, or neither. ANS: even PTS: 1 DIF: Medium REF: 1.1.56 MSC: Numerical Response NOT: Section 1.1 SHORT ANSWER 1. Refer to the graph of the function f in the following figure. f = ( x ) 1 2 3 4 5 6 7 8 –1 –2 –3 –4 x 1 2 3 4 5 –1 –2 –3 –4 –5 y a. Find f (1). b. Find the value of x for which (i) and (ii) . c. Find the domain and range of f . ANS: a. 0 b. ( i ) 2 ( ii ) 1, 3 c. D : [1, 4], R : [ – 3, 1]

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    PTS: 1 DIF: Easy REF: 1.1.3a MSC: Short Answer NOT: Section 1.1 2. If f ( x ) = find f ( – 4), f (0), and f (1). ANS: f ( – 4) = 19, f (0) = 3, f (1) = 1. PTS: 1 DIF: Easy REF: 1.1.19 MSC: Short Answer NOT: Section 1.1 3. Determine whether the function is even, odd, or neither. ANS: Odd PTS: 1 DIF: Medium REF: 1.1.63 MSC: Short Answer NOT: Section 1.1

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    Stewart_Essential Calc_2ET ch01sec02 MULTIPLE CHOICE 1. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. What is the F - intercept and what does it represent? a. 0, Fahrenheit temperature corresponding to b. , Fahrenheit temperature corresponding to c. , Celsius temperature corresponding to d. 32, Celsius temperature corresponding to e. 32, Fahrenheit temperature corresponding to ANS: E PTS: 1 DIF: Medium REF: 1.2.9b MSC: Bimodal NOT: Section 1.2 2. The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her to drive mi and in July it cost her to drive mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model. a. b. c. d. e. ANS: C PTS: 1 DIF: Medium REF: 1.2.14a MSC: Bimodal NOT: Section 1.2 3. Many physical quantities are connected by inverse square laws , that is, by power functions of the form . In particular, the illumination of an object by a light source is inversely prop ortional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move

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    the distance to the lamp. How much brighter is the light? a. times b. times c. 9 times d. times e. times ANS: C PTS: 1 DIF: Medium REF: 1.2.15 MSC: Bimodal NOT: Section 1.2 NUMERIC RESPONSE 1. The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. Complete the table and find the slope. ANS: ; slope = PTS: 1 DIF: Medium REF: 1.2.9a MSC: Numerical Response NOT: Section 1.2 2. It makes s ense 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

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    (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. ANS: a) species b) PTS: 1 DIF: Medium REF: 1.2.16 MSC: Numerical Response NOT: Section 1.2

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    Stewart_Essential Calc_2ET ch01sec03 MULTIPLE CHOICE 1. Use the graph of the function to state the value of , if it exists. a. b. c. d. does not exist e. ANS: D PTS: 1 DIF: Medium REF: 1.3.15 MSC: Bimodal NOT: Section 1.3 2. Use the graph of the function to state the value of if it exists. a. b. c. d. 1 e. does not exist ANS: E PTS: 1 DIF: Medium REF: 1.3.18 MSC: Bimodal NOT: Section 1.3

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    3. Estimate the value of the following limit by graphing the function . Round your answer correct to two decimal places. a. b. c. d. 3.18 e. ANS: E PTS: 1 DIF: Medium REF: 1.3.20a MSC: Bimodal NOT: Section 1.3 NUMERIC RESPONSE 1. By graphing the function and zooming in toward the point where the graph crosses the y - axis, estimate the value of ANS: PTS: 1 DIF: Medium REF: 1.3.19a MSC: Numerical Response NOT: Section 1.3 2. Evaluate the function at the given numbers (correct to six decimal places). Use the results to guess the value of the limit

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    ANS: PTS: 1 DIF: Medium REF: 1.3.21a MSC: Numerical Response NOT: Section 1.3 SHORT ANSWER 1. Complete the table by computing at the given values of x , accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places. x ANS: x – 0.34483 – 0.33445 – 0.33344 – 0.33322 – 0.33223 – 0.32258 – 0.333 PTS: 1 DIF: Medium REF: 1.3.11 MSC: Short Answer

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    NOT: Section 1.3 2. Complete the table by computing at the given values of x , accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places. x 4.9 4.99 4.999 5.001 5.01 5.1 ANS: x 4.9 4.99 4.999 5.001 5.01 5.1 0.1001 0.10001 0.1 0.1 0.09999 0.0999 0.1 PTS: 1 DIF: Medium REF: 1.3.12 MSC: Short Answer NOT: Section 1.3 3. Complete the table by computing at the given values of x , accurate to five decimal places. Use the results to guess at the indicated limit, if it exists, to three decimal places. ANS: 0.20858 0.20008 0.2 0.2 0.20008 0.20858 0.2 PTS: 1 DIF: Medium REF: 1.3.13 MSC: Short Answer NOT: Section 1.3

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