SECTION 1.4 GRAPHING CALCULATORS AND COMPUTERS
29. g(x) = x3 /10 is larger than f(x) = 10x2 30. f (x) = x4 100x3 is larger than g (x) = x3
wheneverx > 100. wheneverx > 101.
300,000 g f 2,000,000 f g
0 / 200 0 150
1,ooo,ooo
31. (a) (i) [0, 5] by [0,2

18 CHAPTER 1 FUNCTIONS AND MODELS
17. y = % sin (x - %): Start with the graph of y = sinx, shift % units to the right, and then compress vertically by a
factor of 3.
18. y =_ 2 + : Start with the graph of y = 1 /x, shift 1 unit left, and then shift

36
magnets EXE R C I S ES
CHAPTER 1 FUNCTIONS AND MODELS
1. (a) Whenx = 2, y z 2.7. Thus, f(2) z 2.7.
(b) f(x) :3 => x ~23, 5.6
(c) The domain off is 6 5 x 5 6, or [6, 6].
(d) The range off is 4 5 y 5 4, or [4, 4].
(e) f is increasing on (4, 4).

SECTION 2.2 THE LIMIT OF A FUNCTION
6x _ 2x
34. (a) From the following graphs, it seems that Inn) , z 1.10. (b)
x> x
4 1.25
1.085052
1.097248
1.098476
1.098749
_ 1.
1 0 1 0.1 0.9 0.1 099978
1.112353
35. For f(x) = x2 (rt/1000):
(a) 0)
0.998000 0.000

28 El CHAPTER1 FUNCTIONS AND MODELS
9. f (x) = 0le3 x2 + 5. Graphing f in a standard viewing
rectangle, [10, 10] by [ 10, 10], shows us what appears to be a
parabola. But since this is a cubic polynomial, we know that a larger
2000
. . I I ' . _50 l-. 150

16 I: CHAPTER1 FUNCTIONS AND MODELS
7. The graph of y = f (x) = 43x x2 has been shifted 4 units to the left, reected about the x-axis, and shied
downward 1 unit. Thus, a function describing the graph is
y= -1-f(x+4) 1
v V
reect shift shift
about 4 units 1

CHAPTER 1 FUNCTIONS AND MODELS
55. (a) R(%) (C) T(in dollars)
l 5 0 2500
10
1000
0 10,000 20.000 I (in dollars) 10,000 20,000 30,000 I(in dollars)
(b) On $14,000, tax is assessed on $4000, and 10% ($4000) = $400.
On $26,000, tax is assessed

32 CHAPTER 1 FUNCTIONS AND MODELS
P (x) = 3x5 5x3 + 2x,
Q (x) = 3x5. These graphs are
signicantly different only in the
region close to the origin. The larger a
viewing rectangle one chooses, the
more similar the two graphs look.
35. (a) The root func

10.
11.
12.
13.
CHAPTER 1 FUNCTIONS AND MODELS
Example 3: A certain employee is paid $8.00 per hour and works a Pay
maximum of 30 hours per week. The number of hours worked is 3:2
rounded down to the nearest quarter of an hour. This employees 236

SECTION 2.2 THE LIMIT OF A FUNCTION :1
29. (a)
l.l4 . 0.42
0.9 3.69 1.1 3.02
0.99 33.7 1.01 33.0
0.999 333.7 1.001 333.0
0.9999 3333.7 1.0001 3333.0
0.99999 33,333.7 1.00001 33,3333
From these calculations, it seems that lim f (x) 2 00 and lim f (x) = 0

10
CHAPTER 1 FUNCTIONS AND MODELS
5. (a) An equation for the family of linear
functions with slope 2 is
y = f(x) = 2x + b, where b is the
y-intercept.
(b) f (2) = 1 means that the point (2, 1) is on the graph of f.
We can use the point-slope for

SECTION 1.2 MATHEMATICAL MODELS
18. By looking at the scatter plot of the data, we rule out the linear and logarithmic models.
610 Cost (in 3)
45 100
(Reduction %)
Scatter plot
We try various models:
Quadratic: y = 0.498x2 ~ 62.289_3x + 1970.65
Cubic: y

(d)
CHAPTER1 REVIEW E
9. (a) The domain of f + g is the intersection of the domain of f and the domain of g; that is, A n B.
(b) The domain of fg is also A n B.
(c) The domain of f / g must exclude values of x that make g equal to O; that is, cfw_x e

SECTION 1.1 FOUR WAYS TO REPRESENT A FUNCTION E 3
14. The temperature of the pie would increase rapidly, level 15. Height
f ass
off to oven temperature, decrease rapidly, and then level 0 gr
off to room temperature. /
T
Wed. Wed. Wed. Wed. Wed.
16-

SECTION 2.2 THE LIMIT OFAFUNCTION 3
11. 1-5 (a) lim f(x) :1
x->0
'I
A (c) Iim f (x) = 0 does not exist because the limits in part (a) and
x->0
2
- part (b) are not equal.
12. lim f (x) exists for all a except a = :L-l.
xm
13.
xll
15.Forg(x)= 3 1.
x _

60 CHAPTER 2 LIMITS AND RATES OF CHANGE
49. The graph of f (x) = [x]| + IIx] is the same as the graph of g (x) = l with holes at each integer, since
f(a) = 0 for any integer a. Thus, lit; f(x) = l and lim f(x) = 1, so limzf(x) = -l.
x> x->
x>2+
f(2) = I

20 Cl CHAPTER1 FUNCTIONS AND MODELS
28. The most important features of the given graph are the x-intercepts and the
maximum and minimum points. The graph of y = 1 / f (x) has vertical
asymptotes at the x-values where there are x-intercepts on the graph of

Principles of Problem Solving
1. By using the area formula for a triangle, % (base) (height), in two ways, we
4
see that % (4) (y) = % (h) (a), so a = 33. Since 42 + y2 = hz,
4Vh2 16
y = m, and a = h .
. P2 100
2. Refer to Example 1, where we obtain

SECTION 2.3 CALCULATING LIMITS USING THE LIMIT LAWS
40. (a)
6.6
_
5.92531
5.99250
5.99925
6.07531
_
6.00750 0 75.4 1-3
6.00075
From the table and the graph, we guess that the limit is 6.
x31
(b) We need to have 5.5 < J 1 < 6.5. From the graph we obtain th

SECTION 1.4 GRAPHING CALCULATORS AND COMPUTERS
4. f(x) = v8x x2
(a) cfw_4, 4] by cfw_4, 4] (b) cfw_5, 5] by [0, 100]
100
5 5
O
(c) cfw_10, 10] by cfw_10, 40] (d) cfw_2, 10] by cfw_2, 6]
40 6
10 -2
The most appropriate graph is produced in viewing rectan

SECTION 1.3 NEW FUNCTIONS FROM OLD FUNCTIONS El 23
49. Letg(t) = cost and f(t) = J5. Then (fog) (t) = /cost = u (t).
50. Letg(t) = m andf(t) =tant. Then (fog) (t) =tan7rt =u(t).
51. Leth(x) =x2,g(x) =3x,andf(x)= l x. Then (fogoh)(x) = 1 3"2 =H(x).
52. Let

SECTION 1.2 MATHEMATICAL MODELS 11
T2T1 8070 10 1
=~=~=.Soa
N2N1 173 113 60 6
linearequationisTSO:%(N173) 4:) T80=%N%3 4: T:N+%[%=51.11
9. (a) Using N in place of x and T in place of y, we nd the slope to be
(b) The slope of % means that the tempe

E CHAPTER1 FUNCTIONS AND MODELS
1 ifx 5 1
x + 2 ifx 5 -1 .
39.f(x)= 40.f(x)= 3x+2 1f-1<x<1
x2 ifx > 1
7 2x ifx _>_ 1
Domain is R.
42.
Domain is R.
41. Recall that the slope m of a line between the two points (x1, y1) and (x2, y2) is m = y2 yl and an e

24
60.
61.
62.
63.
64.
CHAPTER 1 FUNCTlONS AND MODELS
(c) Starting with the formula in part (b), we replace 120 with 240 to reect the
different voltage. Also, because we are starting 5 units to the right of
t = 0, we replace t with t - 5. Thus, th

'fj
14 CHAPTER 1 FUNCTIONS AND MODELS
20- (a) 260 (T) 6 (In T)
1 4 (1n d)
-2 ._ 4W) '
10 2
The graph of T vs. 01 appears to be that of a power function and the graph of In T vs. 1nd appears to be linear,
so a power model seems reasonable.
(b) T =

11.
12.
13.
14.
15.
16.
PRINCIPLES OF PROBLEM SOLVING E 41
Let d be the distance traveled on each half of the trip. Let t1 and t2 be the times taken for the rst and second halves
of the trip.
For the rst half of the trip we have t1 = d /30 and for the s

O PLANO DE RELAES PBLICAS
O PLANO DE RELAES PBLICAS
Uma campanha de comunicao institucional, tambm chamada
corporate, quando adequada e bem planificada, seja ela low ou high
profile, revela-se sempre um investimento rentvel, e em geral, com
repercusses fa