m1 by Hareem Aslam

CHAPTER 1

Functions SECTION 1.1 1. Answer true or false. Given the equation y = x2 − 10x + 16, the values of x for which y = 0 are 2 and 8. 2. Answer true or false. Given the equation y = x2 − 2x + 4, y ≥ 0 for all x ≥ 0. 3. Answer true or false. Given the equation y = 8 −

√ 3

x, y = 2 when x = 0.

4. Answer true or false. Given the equation y = −x2 + 3x − 4, it can be determined that y has a minimum value. 5. Answer true or false. Referring to the graph of y = value.

√

x2 , y can be determined to have a minimum

6. Assume the temperature of an experiment varies according to y = x2 − 12x, where x represents the time in seconds after the experiment starts. After how many seconds will the temperature ﬁrst become positive? A. 11 s

B. 12 s

C. 13 s

D. 14 s

7. Use the equation y = x2 − 2x − 24. For what values of x is y ≥ 0? A. {x : 4 ≤ x ≤ 6} C. {x : −4 ≤ x ≤ −6}

B. {x : x ≤ −6 or x ≥ 4} D. {x : x ≤ −4 or x ≥ 6}

8. From the graph of y = x3 − x determine for which values(s) of x where y = 0.

A. 0

B. 1

C. 0, 1

D. −1, 0, 1

9. From the graph of y = −2x2 − 4x + 2 determine the maximum value of y.

A. −4

C. −2

B. 4 1

D. 2

True/False and Multiple Choice Questions

10. From the graph of y = 3x2 + 6x − 2 determine at what x the graph has a minimum.

A. 1

B. 2

C. 0

D. −1

11. From the graph of y = x4 − 16 determine for what x values the graph appears to be below the x-axis.

A. (−2, 2)

B. (0, 2)

C. (−5, 0)

D. (−6, 0)

12. Assume it is possible to measure the observations given below. Which, if any, would most likely generate a broken graph? A. B. C. D.

the speed of the wind over a given time period the number of teddy bears made in a day the brightness of a light as the distance from the light changes none of the above

13. Answer true or false. The electricity supplied to a light bulb that is turned on and oﬀ frequently will generate a broken line graph, when plotted against time. 14. A rectangular solid has a prescribed surface area. It would have a minimum volume if A. B. C. D.

the length, width, and height are all equal the length is twice the width, and the height equals the width the length equals the height, and the length is twice the width the length is twice the width and is three times the height.

15. A graph has the shape y = x2 + 8x + 12. It has A. B. C. D.

a maximum only a minimum only both a maximum and a minimum neither a maximum nor a minimum.

16. Use the equation y = 3 − A. 5

√

x to ﬁnd the value of x for which y = −2.

B. 25

C. −5

D. −25

17. Use the equation y = x2 − 4 to ﬁnd the minimum value of y. A. 4

B. 0

C. −4

D. 2

Section 1.2

SECTION 1.2 1. Answer true or false. If f (x) = 4x2 − 4 then f (1) = 0. 2. Answer true or false. If f (x) = 3. f (x) = A. B. C. D.

1 , then f (0) = 0. x2

1 − 2. The natural domain of the function is (x − 1)2

all real numbers all real numbers except 1 all real numbers except −1 and 1 all real numbers except −1, 0, and 1.

4. Use a graphing utility to determine the natural domain of h(x) = A. B. C. D.

2x . |x| − 5

all real numbers all real numbers except 5 all real numbers except −5 and 5 all real numbers except −5, 0, and 5

5. Use a graphing utility to determine the natural domain of g(x) = A. {x : −3 ≤ x ≤ 3} C. {x : x ≥ −9}

√

x2 − 9.

B. {x : x ≤ −3 or 3 ≤ x} D. {x : x ≥ −3}

6. Answer true or false. f (x) = |x + 4| can be represented in the piecewise form by x + 4, if x ≤ 0 f (x) = −x + 4, if x > 0. 7. Find the x-coordinate of any hole(s) in the graph of f (x) = A. 2

B. −2 and 2

x2 − 2x . x2 − 4

C. −2

D. −2, 0, and 2

x2 − 9 and g(x) = x + 3 are identical except f (x) has a hole at x = 3. x−3 π t . Find f (1). 9. Use a graphing device to plot f (t) = tan 4 8. Answer true or false. f (x) =

A. 0

B. 1

C. −1

D. undeﬁned

10. Light intensity varies over time in seconds according to I(t) = 3t2 − t, due to changing voltage. Find the intensity of the light at t = 2 s. A. 10

B. 14

C. 12

D. 1

11. Answer true or false. If a kite is ﬂying at h(t) = sin(tπ) + 20 meters where t is time in seconds, what is the height of the kite at t = 1 s? A. 21 m

B. 20 m

C. 19 m

D. 20.5 m

True/False and Multiple Choice Questions

x 12. The speed of a boat in miles/hour for the ﬁrst 10 minutes after leaving a dock is given by f (x) = . 3 Find the speed of the boat 6 minutes after leaving the dock. A. 18 miles/hour

B. 36 miles/hour

C. 2 miles/hour

D. 6 miles/hour

13. Find f (2) if f (x) = {x3 , if x < 2 and x2 + 1 if x ≥ 2}. A. 2 C. 5

B. 8 D. It cannot be determined.

14. Determine all x-values where there are holes in the graph of f (x) = A. −2, 3

B. −2

x2 + 2x − 15 . (x + 2)(x − 3)2

C. 3

D. none

C. 4

D. 6

C. 9

D. 3

15. If f (x) = 5 + (x − 2)2 , f (3) = A. 25

B. 30

16. f (x) = A. 4

x − 9, x2 ,

x≤3 x>3

Find f (2). B. −7

17. Determine which graph deﬁnes y as a function of x. A.

Section 1.3

SECTION 1.3 1. Answer true or false. If the window on a graphing utility is set with −10 ≤ x ≤ 10 and −10 ≤ y ≤ 10 the graph of f (x) = x2 − 3x + 4 has a minimum that appears in the window. 2. Answer true or false. If the window on a graphing utility is set with −10 ≤ x ≤ 10 and −10 ≤ y ≤ 10 the graph of f (x) = x2 + 12 has a minimum that appears in the window. 3. The smallest domain that is needed to show the entire graph of f (x) = utility is A. −10 ≤ x ≤ 10

B. −5 ≤ x ≤ 5

C. 0 ≤ x ≤ 10

4. The smallest range that is needed to show the entire graph of f (x) = utility is A. 0 ≤ y ≤ 6

B. −6 ≤ y ≤ 6

√

C. 0 ≤ y ≤ 10

100 − x2 on a graphing D. 0 ≤ x ≤ 5.

√

144 − x2 on a graphing D. −12 ≤ y ≤ 12.

5. Answer true or false. If xScl is changed from 1 to 2 it is necessary that yScl also be changed from 1 to 2. 6. Using a graphing utility y = −10 ≤ x ≤ 10 domain? A. 3

x can be determined to have many false line segments on a − 12

B. 0

C. 1

D. 2

7. How many functions are needed to graph the ellipse x2 + 2y 2 = 14 on a graphing utility? A. 1

B. 2

C. 3

D. 4

8. A student tries to graph an ellipse on a graphing utility, but the graph appears to be a circle. To view this as an ellipse the student could A. increase the range of x C. increase xScl

B. increase the range of y D. increase yScl.

   x − 1, if x ≤ 2 x2 , if 2 < x ≤ 4 . This can be 9. Answer true or false. A student wishes to graph f (x) =   3 x , if x > 4 accomplished by graphing three functions, then sketching the graph from the information obtained. 10. The graph of f (x) = A. nowhere

√

x − 2 touches the y-axis B. at 1 point

C. at 2 points

D. at 4 points.

C. at 2 points

D. at 3 points.

11. The graph of f (x) = x2 − 2 crosses the x-axis A. nowhere

B. at 1 point

12. Answer true or false. The graph of f (x) = |x| − 2 is nowhere negative. 13. Which of these functions generates a graph that goes negative? A. f (x) = | cos x|

B. G(x) = | cos |x||

C. h(x) = cos |x|

D. F (x) = | sin x| + | cos x|

True/False and Multiple Choice Questions

14. Answer true or false. The graph of f (x) = of −2 ≤ x ≤ 2 and −5 ≤ y ≤ 5.

√

x + 2 + 5 can be shown on a graphing utility’s window

15. Answer true or false. All windows on graphing utilities must be symmetric about the origin. 16. Which window is best for viewing the graph of the function f (x) = x2 − 15? A.

−10 ≤ x ≤ 10 −10 ≤ y ≤ 10

−10 ≤ x ≤ 10 0 ≤ y ≤ 20

−25 ≤ x ≤ −5 −20 ≤ y ≤ 0

−10 ≤ x ≤ 10 −20 ≤ y ≤ 0

17. The graph of the equation x2 + y 2 = 36 is a circle. Find a function whose graph is the lower semicircle. √ √ √ √ C. y = 36 − x2 D. y = x2 − 36 A. y = − 36 − x2 B. y = − x2 − 36

Section 1.4

SECTION 1.4 1.

The graph on the left is the graph of f (x) = x2 . The graph on the right is the graph of B. y = (f (x) − 4)2

A. y = (f (x) + 4)2 2. The graph of y = 1 + A. B. C. D.

√

C. y = f (x) − 4

x + 2 is obtained from the graph of y =

√

D. y = f (x) + 4.

x by

translating horizontally 2 units to the right, then translating vertically 1 unit up translating horizontally 2 units to the left, then translating vertically 1 unit up translating horizontally 2 units to the right, then translating vertically 1 unit down translating horizontally 2 units to the left, then translating vertically 1 unit down.

3. The graph of y = (x + 1)4 and y = −(x + 1)4 are related. The graph of y = −(x + 1)4 is obtained by A. B. C. D.

reflecting the graph of y = (x + 1)4 about the x-axis reflecting the graph of y = (x + 1)4 about the y-axis reflecting the graph of y = (x + 1)4 about the origin. The equations are not both defined.

√ √ 4. The graphs of y = x and y = −3 x − 2 + 1 are related. Of reflection, stretching, vertical translation, and horizontal translation, which should be done first? A. reflection C. vertical translation

B. stretching D. horizontal translation

5. Answer true or false. f (x) = x2 and g(x) = x + 3. Then f g(x) = x3 + 3x. 6. Answer true or false. f (x) = x and g(x) = x − 2. f /g has the domain (−∞, ∞). 7. f (x) = x3 and g(x) = x − 2. f ◦ g(x) = A. x3 − 2

B. (x − 2)3

√

x3 − 8

√

x4 + 2x3

8. f (x) = |(x + 2)6 | is the composition, f ◦ g(x), of A. f (x) = x + 2; g(x) = |x6 | √ C. f (x) = 6 x + 2; g(x) = |x6 |

B. f (x) = (x + 2)6 ; g(x) = |x6 | D. f (x) = x6 ; g(x) = |x + 2|.

9. f (x) = x − 2. Find f (2x). A. 2x − 4

B. 2x − 2

x−2 2

D. 2x2 − 2x

10. f (x) = x2 + 2. Find f (f (x)). A. x4 + 4

B. 4x2 + 4

C. x4 + 4x2 + 4

D. x4 + 4x2 + 6

True/False and Multiple Choice Questions

11. f (x) = sin x is A. an even function only C. both an even and an odd function

B. an odd function only D. neither an even nor an odd function.

12. f (x) = 1 is A. an even function only C. both an even and an odd function

B. an odd function only D. neither an even nor an odd function.

13.

The function graphed above is A. an even function only C. both an even and an odd function 14. Answer true or false. f (x) =

√

B. an odd function only D. neither an even nor an odd function.

x2 − sin x is an even function.

15. f (x) = x2 + 5 cos x is symmetric about A. the x-axis

B. the y-axis

C. the origin

D. nothing.

C. the origin

D. nothing.

C. x6 − 6

D. x5 − 6

16. f (x) = x3 − sin x is symmetric about A. the x-axis

B. the y-axis

17. f (x) = tan x − 3 sin x is A. B. C. D.

an even function an odd function both an even function and an odd function neither an even function nor an odd function.

18. f (x) = x2 and g(x) = x3 − 6. f ◦ g(x) = A. x5 − 6x2

B. (x3 − 6)2

Section 1.5

SECTION 1.5 1. Answer true or false. The points (2, 3), (3, 5), and (5, 9) lie on the same line. 2. A particle, initially at (−2, 1), moves along a line of slope m = 3 to a new position (x, y). Find y if x = 2. A. 8

B. 13

C. 16

D. 5

3. Find the angle of inclination of the line −4x − 6y = 2 to the nearest degree. A. 56◦

B. −56◦

C. 34◦

D. −34◦

4. The slope-intercept form of a line having a slope of 6 and a y-intercept of 2 is A. x = 6y + 2

B. y = 6x + 2

C. y = −6x − 2

D. x = −6y − 2.

5. Answer true or false. The lines y = 2x + 4 and y = 2x + 1 are parallel. 6. Answer true or false. The lines y = x + 3 and x + y = 4 are perpendicular. 7.

The slope-intercept form of the equation of the graphed line is A. y = 2x − 5

B. y = 2x + 5

C. y = −2x + 5

D. y = −2x − 5.

8. A particle moving along an t-axis with a constant velocity is at the point x = 1 when t = 0 and x = 2 when t = 4. The velocity of the particle if x is in meters and t is in seconds is A. 4 m/s

B. −4 m/s

1 m/s 4

D. −

1 m/s. 4

9. Answer true or false. A particle moving along an t-axis with constant acceleration has velocity v = 4 m/s at time t = 1 s and velocity v = 6 m/s at time t = 2 s. The acceleration of the particle is 4 m/s2 . 10. Answer true or false. A baseball is pitched at 90 mi/hr and hit by a batter to second base at 96 mi/hr. The average speed of the ball is 93 mi/hr. 11. Answer true or false. A spring is stretched from its natural length 20 cm by a 20-N force. How much would it stretch if a 60-N force were applied to it instead? A. 30 cm

B. 60 cm

C. 120 cm

D. 40 cm

12. Answer true or false. A particle moves with a velocity, in cm/s, according to the equation v = t3 −2t. At t = 1 the velocity is A. 2 cm/s

B. 1 cm/s

C. 0 cm/s

D. −1 cm/s.

True/False and Multiple Choice Questions

13. Answer true or false. A particle moves with an acceleration in cm/ss given by a = 3t2 + 2t. At t = 3 the acceleration is A. 33 cm/s2

B. 9 cm/s2

C. 5 cm/s2

D. 18 cm/s2 .

14. Power in watts for a circuit is given by P = I 2 R, where I is the current in amperes. A certain circuit has a constant value of resistance, R, given by R = 1 − Ω. Find the power when the current is 2 amperes. A. 2 w

B. 20 w

C. 40 w

D. 100 w

15. Answer true or false. A spring has a natural length of 1.0 m. If 5 kg is hung from the spring, the spring stretches to 1.1 m. If an additional 5 kg is added to the mass hanging from the spring the length of the spring increases to 2.2 m. 16. Find the equation of the line parallel to y = 5x − 6 that passes through (1, 4). A. y = 5x − 1

B. y = 5x − 9

1 C. y = − x − 1 5

1 D. y = − x − 9 5

17. Find the equation of the line perpendicular to y = 5x − 6 that passes through (5, −6). A. y = 5x − 1

B. y = 5x − 9

1 C. y = − x − 5 5

1 D. y = − x − 9 5

Section 1.6

SECTION 1.6 1. What do all members of the family of lines of the form y = ax + 2 have in common? A. B. C. D.

Their slope is 2. Their slope is −2. They go through the origin. They cross the y-axis at the point (0, 2).

2. What points do all graphs of equations of the form y =

√ n

x, n is even, have in common?

A. (0, 0) only C. (−1, −1), (0, 0), and (1, 1)

B. (0, 0) and (1, 1) D. none

The equation whose graph is given is √ √ A. y = x B. y = 3 x

C. y =

1 x2

D. y =

1 . x3

4. Answer true or false. The graph of y = −2(x + 5)1/3 can be obtained by making vertical and horizontal shifts of the graph of y = x + 5. 5. Answer true or false. The graph of y = x2 − 4x + 4 can be obtained by transforming the graph of y = x2 to the right 2 units 6. Answer true or false. There is no diﬀerence in the graphs of y = 7. Determine the vertical asymptote(s) of y = A. x = −6, x = 3

A. x = 0

√ |x| and y = | 3 x|.

x . x2 + 3x − 18

B. x = 6

8. Find the vertical asymptote(s) of y =

C. x = −3, x = 6

D. x = 3

C. x = 2

D. x = −2, x = 0

x−1 . x2 + 2x

B. x = 0, x = 2

9. For which of the given angles, if any, is the sin and tan positive and the cos negative? 2π 3

π 3

4π 3

D. No such angle exists.

10. Use the trigonometric function of a calculating utility set to the radian mode to evaluate tan A. 0.0110

B. 0.0000

C. 0.7265

D. 0.8241

π 5

True/False and Multiple Choice Questions

11. A cylinder is turned on its side and rolls. The cylinder has a diameter of 4.00 m turns through an angle of 180◦ . How far does the cylinder travel? A. 6.28 m

B. 200 m

C. 2.00 m

D. 4.00 m

12. Answer true or false. The amplitude of sin(2x − π) is 2. π π is − . 13. Answer true or false. The phase shift of 6 cos x − 3 3 π 2π 14. Answer true or false. The period of y = sin 5x − is . 3 5 15. Answer true or false. A force acting on an object, F = kx2 , that is directly proportional to the square of the distance from the object to the source of the force is found to be 25 N when x = 1 m. The force will be 100 N if x becomes 2 m. 16. Find the period of sin 2x. A. 2π

B. 4π

C. π

D. 2

C. 3

D. 6

17. Find the amplitude of −3 + 4 sin x. A. 4

B. 8

Section 1.7

SECTION 1.7 1. Answer true or false. An object’s position from the origin is given by the accompanying table. Using the quadratic regression feature of a calculator, the position equation is best given by s(t) = 3.2t2 − 6.5t − 62.0. Time (sec) 0 1 2 3 4 5 6

position (cm) −62.0 −65.3 −62.2 −52.7 −36.8 −14.5 −14.2

2. Answer true or false. An object’s position from the origin is given by the accompanying table. Using the quadratic regression feature of a calculator, the position equation is best given by s(t) = 5.4t2 − 6.8t − 6.0. Time (sec) 0 1 2 3 4 5 6

position (cm) −6.0 6.2 29.2 63.0 107.6 163.0 229.2

3. Answer true or false. An object’s position from the origin is given by the accompanying table. Using the linear regression feature of a calculator, the position equation is best given by s(t) = 7.3t − 3.4. Time (sec) 0 1 2 3 4 5 6

position (cm) −3.4 3.9 11.2 18.5 25.8 33.1 40.4

AUTHOR: PLEASE PROVIDE MISSING ITEMS 4, 5, AND 6

True/False and Multiple Choice Questions

7. A metal rod’s length varies with its temperature according to the table. What is the correlation coeﬃcient for this collection of data points? Temperature (◦ C) 72 78 84 90 96 A. 0.995

B. 0.996

length (m) 5.00 5.11 5.23 5.35 5.49 C. 0.998

D. 0.999

8. The accompanying table gives the number of centimeters a spring is stretched by various attached weights. Use a linear regression to express the amount of stretch of the spring as a function of the weight attached. Weight (N) 0.0 0.5 1.0 1.5 2.0 2.5 A. S = 2.70W t − 4.76 C. S = 2.70W t

Stretch (cm) 0.0 1.37 2.68 3.99 5.39 6.74 B. S = 2.70W t + 4.76 D. S = 2.60W t + 5.00

9. The accompanying table gives the number of centimeters a spring is stretched by various attached weights. Use a linear regression to determine the correlation coeﬃcient. Weight (N) 0.0 0.5 1.0 1.5 2.0 2.5 A. 0.996

B. 0.997

Stretch (cm) 0.0 1.37 2.68 3.99 5.39 6.74 C. 0.999

D. 1.00

Section 1.7

10. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6 A. quadratic

B. linear

position (cm) 1.5 2.2 18.9 51.6 100.3 165.0 245.7 C. sine

D. none of these.

11. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6 A. quadratic

B. linear

position (cm) â&#x2C6;&#x2019;3.614 4.513 12.640 20.767 28.894 37.021 45.148 C. sine

D. none of these.

12. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6 A. quadratic

B. linear

position (cm) 7.0000 3.0200 6.9203 3.1777 6.6877 3.4806 6.3206 C. sine

D. none of these.

True/False and Multiple Choice Questions

13. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 A. quadratic

B. linear

position (cm) 3.6674 4.7757 6.6315 3.0503 5.9666 5.6616 C. sine

D. none of these.

14. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6 A. quadratic

B. linear

position (cm) 6.15 14.07 21.99 29.91 37.83 45.75 53.67 C. sine

D. none of these.

15. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6 A. quadratic

B. linear

position (cm) â&#x2C6;&#x2019;6.27 2.99 12.25 21.51 30.77 40.03 49.29 C. sine

D. none of these.

Section 1.8

SECTION 1.8 π t (0 ≤ t ≤ 4), where t is time in seconds, describe the motion of particle, 1. If x = t2 and y = sin 2 then the x- and y-coordinates of the position of the particle at time t = 5 are A. (25, −1)

B. (25, 1)

C. (25, 0)

D. (5, 0).

2. Answer true or false. Given the parametric equations x = 2t and y = 6t + 2, eliminating the parameter t gives y = 3x + 2. 3. Use a graphing utility to graph x = 6 sin t and y = 3 cos t(0 ≤ t ≤ 2π). The resulting graph is A. A circle

B. A hyperbola

C. An ellipse

D. A parabola.

4. Identify the equation in rectangular coordinates that is a representation of x = 3 cos t, y = 2 sin t (0 ≤ t ≤ 2π). A. 3x2 + 2y 2 = 1

B. 9x2 + 4y 2 = 1

x2 y2 + =1 3 2

x2 y2 + =1 9 4

5. Answer true or false. The graph in the rectangular coordinate system of x = sin t, y = tan t (0 ≤ t ≤ π/2) is an ellipse. 6. Answer true or false. The parametric representation of x2 + y 2 = 4 is x = 2 sin t, y = 2 cos t (0 ≤ t ≤ 2π). 7. The circle represented by x = 5 + 2 cos t, y = 1 + 2 sin t (0 ≤ t ≤ 2π) is centered at A. (1, 5)

B. (5, 1)

C. (−1, −5)

D. (−5, −1).

8. Answer true or false. The trajectory of a particle is given by x = t2 , y = t has the shape of a parabola that opens upward. 9. Answer true or false. x = t, y = t (1 ≤ t ≤ 3) is the parametric representation of the line segment from P to Q, where P is the point (1, 1) and Q is the point (3, 3). 10. x = t, y = a, where a is a constant, is the parametric representation of a A. horizontal line C. line with slope +1

B. vertical line D. line with slope −1.

11. Use a graphing utility to graph x = −2y 2 + 3y + 6. The resulting graph is a parabola that opens A. upward

B. downward

C. left

D. right.

12. Answer true or false. x = t2 − 1, y = 3t represents a curve passing through the point (0, 3). 13. The parametric form of a vertical line passing through (3, 0) is A. x = t, y = 3

B. x = 3, y = t

C. x = t, y = −3

D. x = −3, y = t.

14. Answer true or false. The curve represented by the piecewise parametric equation x = 5t, y = 2t (0 ≤ 2); x = 5t3 , y = 2 (2 < t ≤ 4) can be graphed as a continuous curve over the interval (0 ≤ t ≤ 4).

True/False and Multiple Choice Questions

15. Answer true or false. An arrow is shot at an angle of 60◦ above the horizontal with an initial speed v0 = 70 m/s. The arrow will rise 188 m (rounded to the nearest meter). 16. x = 3t + 2, y = 4t − 1 where 0 ≤ t ≤ 2 is a line segment from what point to what point? A. (0, 0) to (2, 2) C. (2, 8) to (−1, 7)

B. (2, −1) to (8, 7) D. (0, 0) to (8, 7)

Chapter 1 Test

CHAPTER 1 TEST 1. Answer true or false. For the equation y = x2 − 11x + 24, the values of x that cause y to be zero are −3 and 8. 2. Answer true or false. The graph of y = x2 − 2x + 6 has a maximum value. 3. A company has a profit/loss given by P (x) = 0.1x2 − 4x − 10,000, where x is time in days, good for the first 20 years. After how many days (rounded to the nearest day) will the graph of the profit/loss equation become 0? A. 426 days

B. 400 days

C. 320 days

D. 337 days

4. Use a graphing utility to determine the natural domain of g(x) =

5 . (x − 3)3

A. all real numbers

B. all real numbers except 3

C. all real numbers except −3

D. all real numbers except −3 and 3

5. Answer true or false. If f (x) = x3 , then f (1) = 1. 6. Find the hole(s) in the graph of f (x) =

x−2 . x2 − 4

B. x = −2

A. x = 2

C. x = −2, 2

D. x = −2, 0, 2

t2 7. A worker completes n(t) = + 2t + 1 items after t hours of work on a production line, where t 25 is time given in hours. How many items does the person complete in the ﬁrst 5 hours of work? A. 12

B. 11

C. 10

8. Use a graphing utility to determine the entire domain of f (x) = A. all real numbers

B. 0 ≤ x ≤ 16

D. 36 √

256 − x4 .

C. −16 ≤ x ≤ 16

D. −4 ≤ x ≤ 4

9. Answer true or false. The graph of f (x) = |x − 4| touches the x-axis exactly once. 10. Answer true or false. The graph of y = the domain −10 ≤ x ≤ 10.

x3 − 1 has a false line segment on a graphing utility on x

11. The graph of y = x3 + 2 is obtained from the graph of y = x3 by A. B. C. D.

translating vertically 2 units upward translating vertically 2 units downward translating horizontally 2 units to the left translating horizontally 2 units to the right.

12. If f (x) = A. x

√

x and g(x) = x4 , x ≥ 0, then g ◦ f (x) = B. x2

C. x8

13. Answer true or false. f (x) = |x| + x2 is an even function.

√ 8

True/False and Multiple Choice Questions

14. A particle initially at (0, 3) moves along a line of slope m = 5 to a new position (x, y). Find y if x = 5. A. 25

B. 28

C. 3

D. 5

15. The slope-intercept form of a line having a slope of 2 and a y-intercept of 4 is A. x = 2y + 4

B. x = 2y − 4

C. y = 2x + 4

D. y = 2x − 4.

16.

The equation whose graph is given is A. y = x3

B. y = −x3

C. y =

17. Answer true or false. The only asymptote of y =

√ 3

√ D. y = − 3 x.

x is y = 0. x2 + x + 1

18. A ball of radius 2 cm rolls through an angle of 30◦ . How far does the ball travel while rolling through this angle? (Round to the nearest hundredth of a centimeter.) A. 0.52 cm

B. 1.05 cm

C. 4.19 cm

D. 8.38 cm

19. If x = 2t and y = sin(πt) (0 ≤ t ≤ 2), where t is time in seconds, describe the motion of a particle, the x- and y-coordinates of the position of the particle at t = 0.5 s are A. (1, 0)

B. (−1, 1)

C. (0, 1)

D. (1, 1).

20. The ellipse represented by x = 2 cos t, y = 4 sin t (0 ≤ t ≤ 2π) is centered at √ A. (2, 4) B. (−2, −4) C. ( 2, 2) D. (0, 0). 21. The graph of x = 6 + 3 cos t, y = 7 + 5 sin t (0 ≤ t ≤ 2π) is A. a circle

B. a hyperbola

C. an ellipse

D. a parabola.

22. A particles has a position function t seconds after an experiment begins given by the accompanying table. The position function is close to Time (sec) 0 1 2 3 4 5 6

A. quadratic

B. linear

position (cm) 8.15 16.07 23.99 31.91 39.83 47.75 55.67

C. sine

D. none of these.

SOLUTIONS

SECTION 1.1 1. T 13. T

2. T 3. F 4. F 5. T 6. B 14. A 15. B 16. B 17. C

7. D

8. D

9. B

10. D

11. A

12. B

7. A

8. T

9. B

10. A

11. B

12. C

7. B

8. A

9. T

10. A

11. C

12. F

2. B 3. A 4. D 5. F 6. F 7. B 14. F 15. B 16. C 17. B 18. B

8. D

9. B

10. D

11. B

12. A

7. B

8. C

9. F

10. F

11. B

12. D

7. A

8. D

9. D

10. C

11. A

12. F

SECTION 1.2 1. T 13. C

2. F 3. B 4. C 5. B 6. F 14. A 15. D 16. B 17. A

SECTION 1.3 1. T 13. C

2. F 3. A 4. D 5. F 6. D 14. F 15. F 16. D 17. A

SECTION 1.4 1. C 13. A

SECTION 1.5 1. T 13. A

2. B 3. D 4. B 5. T 6. T 14. C 15. F 16. A 17. C

SECTION 1.6 1. D 13. F

2. B 3. C 4. F 5. T 6. T 14. T 15. T 16. C 17. A

SECTION 1.7 1. F 13. C

2. T 3. T 4. T 14. A 15. B

5. F

6. D

7. C

8. C

9. D

10. A

11. B

12. C

2. T 3. C 4. D 5. F 14. F 15. T 16. B

6. T

7. B

8. F

9. T

10. A

11. C

12. T

2. F 3. D 4. B 5. T 6. A 7. A 14. B 15. C 16. B 17. T 18. B

8. D 19. A

SECTION 1.8 1. B 13. B

CHAPTER 1 TEST 1. F 13. T

9. T 10. T 11. A 12. B 20. D 21. C 22. A