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Unformatted text preview: 16 Chapteri ‘ Functions and Graphs Graph
1.y=4 2.y=—3.5
3.x=—4.5 4.x=10 Graph. Find the slope and the y—intercept. 5.y=—3x 6.y=—O.5x
7.y=0.5x 8.y=3x
9.y=—2x+3 10.y=—x+4
11.y=—x—2 12.y=—3x+2 Find the slope and the yintercept.
13.2x+y—2=0 14.2x—y+3=0
15.2x+2y+5=0 16.3x—3y+6=0
17.x=2y+8 18.x=—4y+3 Find an equation of the line: 19. with m = —5, containing (1, —5).
20. with m = 7, containing (1, 7). 21. with m = —2, containing (2, 3).
22.. with m = '3, containing (5, 2).
23. with slope 2, containing (3, 0). 24. with slope —5, containing (5, O).
25. with y—intercept (O, ~6) and slope
26. with y—intercept (O, 7) and slope g.
27. with slope 0, containing (2, 3). 28. with slope 0, containing (4, 8). Find the slope of the line containing the given pair of
points, if it exists. 29. (—4, —2) and (2, 1) 30. (‘2, l) and (6, 3) 31. (in i) and (r3, ‘5‘) 32 H, 3) and (3, 13—6) 33. (3, —7) and (3, 9) 34. (4, 2) and (—4, 10) 35. (2, 3) and (—1, 3) 36. (6, i) and (—7, §)
37. (x, 3x) and (x + h, 3(x + 11))
38. (x, 4x) and (x + h, 4(x + 11)) 39. (x, 2x + 3) and (x + h, 2(x + h) + 3)
40. (x, 3x ~ 1) and (x + h, 3(x + h)  1) 41.—52. Find an equation of the line containing the
pair of points in each of Exercises 29—40. 53. Find the slope (or grade) of the treadmill. 0.4 f Ie—Fh 5 ft~———>1 54. Find the slope (or pitch) of the roof. 55. Find the slope (or head) of the river. 1238 ft 56. North Carolina state law requires that stairs have
minimum treads (or Width) of 9 in. and maximum
risers (or height) of 8.25 in" According to North
Carolina law, What is the maximum grade of stairs in North Carolina? 4North Carolina Office of the State Fire Marshall. 57. Find the average rate of change of life expectancy at
birth.5 3’
77.0 (2000, 76.9) .
76.5 r ‘ 76.0
75.5
75.0
74.5
74.0
73.5 Life expectancy (1980, 73.7) I    >
I 1985 1990 1995 2000 x
Year of birth 58. (Scisim and Faint/1229mm. If the temperature is C de
grees Celsius, then the temperature is also F de—
grees Fahrenheit, where 9
F(C) = ;C + 32. a) Find F(—10), F(O), F(10), and F(40). b) Suppose the outside temperature is 30 degrees
Celsius. What is the temperature in degrees
Fahrenheit? c) What temperature is the same in both degrees
Fahrenheit and in degrees Celsius? 59. Margy {.ftmsermtion. The R~factor of home insula
tion is directly proportional to its thickness T. a) Find an equation of variation if R = 12.51 when
T = 3 in. b) What is the Rfactor for insulation that is 6 in.
thick? 60. Nerve litiptzlse .Sprted. Impulses in nerve fibers travel
at a speed of 293 ft/ sec. The distance D traveled in
t seconds is given by D = 293t. How long would it
take an impulse to travel from the brain to the toes
of a person who is 6 ft tall?
61. 13mm Wight, The weight B of a human’s brain is
directly proportional to his or her body weight W.
a) It is known that a person who weighs 200 lb has
a brain that weighs 5 lb. Find an equation of
variation expressing B as a function of W.
b) Express the variation constant as a percent and
interpret the resulting equation.
c) What is the weight of the brain of a person who
weighs 120 lb? 5National Center for Health Statistics. 1.1 Slope and Linear Functions 17 62. Masdv ‘V/EV/élgggli. The weight M of the muscles in a
human is directly proportional to his or her body
weight W. a) It is known that a person who weighs 200 lb has
80 lb of muscles. Find an equation of variation
expressing M as a function of W. b) Express the variation constant as a percent and
interpret the resulting equation. c) What is the muscle weight of a person who
weighs 120 lb? Muscle weight is directly proportional to body weight. 63. Steppin Distance rm Glare lrtc. The Stopping dis
tance (at some fixed speed) of regular tires on glare
ice is given by D(F) = 2F + 115, where D(F) is the stopping distance, in feet, when
the air temperature is F, in degrees Fahrenheit. 200 150
D(F) = 2F + 115 a) Find D(O°), D(—20°), D(10°), and D(32°).
tW b) Explain why the domain should be restricted to
the interval [~57.5°, 32°]. 64. Retailers Time. While driving a car, you see a per~
son suddenly cross the street unattended. Your
brain registers the emergency and sends a signal to
your foot to hit the brake. The car travels a distance
D,.in feet, during this time, where D is a function of Using the same set of axes, graph the pair of equations. 1. y = %x2 andy = —%x2
2. y = ﬁxz andy = —%x2 .y=x2andy=(xM1)2
.y=x2andy=(x~3)2 3
4
5.y=x2andy=(x 1)2
6.y=x2andy=(x 3)2
7 .y=x3andy=x31 8.y=x3andy=x3—1 For each of the following, state whether the graph of
the function is a parabola. If the graph is a parabola,
then find the parabola’s vertex. 9.y=x2+4x—7 10.y=x3—2x+3
11.y=2x4—4x2~3 12.y=3x2—6x Graph.
l3.y=x2—4x+3 15.y=—x2+2x~1
17.y=2x2+4x—7
19.y=%x2+3x—5 14.y=x2—6x+5 16.y=—x2—x+6
18.y=3x2—9x+2
20.y=§x2+4x2 Solve.
21. x2 — 2x = 2 23.3y2+8y+2=0 22.x2—2x+1=5
24.2p2~5p=1 Solve. Some of your answers may involve i.
25.x2—2x+10=0 26.x2+6x+10=0 27.x2+6x=1 28.x2+4x=3
29.x2+4x+8=0 30.x2+10x+27=0
31. 4x2=4x+ 1 32. —4x2=4x— 1 1 5:31 33. 3‘1 itéi Making. The number of oranges stacked in a
pyramid is approximated by the function
1 3 1 2 1
ﬁx) 6 x 2 x 3 x, where f (x) is the number of oranges and x is the
number of layers. Find the number of oranges
when the number of layers is 7, 10, and 12. 1.2‘ Polynomial Functions 29 34. f The average payroll P (in millions of
dollars) for teams in the National Basketball Associ
ation (NBA) can be approximated by P = 4.8565 + 0.284lx + 0.1784x2, where x is the number of years since the 1985—86
season. a) Estimate the average payroll for the 2009—10
season. b) Use the quadratic formula to predict when the average NBA payroll will be $ 100 million. 1532’
{H 35. .< , ‘ The average ticket price for a
major league baseball game can be modeled by the
function p(x) = 9.41 — 0.19x + 0.09x2, where x is the number of years after 1990.6 Use the quadratic formula to predict when the average price
of a ticket will be $50. , , The target weight w for an adult
man of medlum build is w(h) = 0.0728112 — 6.98671 + 289, where h is in inches (for 62 3 h S 76) and w is in
pounds.7 21) Find the target weight of an adult man of
medium build who is 6 ft (72 in.) tall. b) If a man of medium build has achieved his target
weight of 170 1b, how tall is he? 37. Let f(x) = x3 — x2. tW a) For very large values of x, is x
Explain.
tw b) Use (a) to describe what f(x) looks like when x
is very large.
c) Use a grapher to plot the graph of for
100 S x S 200. Does the graph confirm (b)? 38. Let f(x) = x4 ~ 10x3 + 3x2 — 2x + 7. UN a) For very large values of x, is x4 or —10x3 + 3x2 — 2x + 7 larger? Explain.
tw b) Use (a) to describe what f(x) looks like when x
is very large. 3 or x2 larger? 6Major League Baseball.
7Metropolitan Life Insurance Company. ...
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 Fall '11
 JosephChen

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