Table Of ContentSection 1.1 1
Chapter 1 Section 1.1 Exercises
Prerequisites for Calculus
1. Dx52121522
Dy52122 523
n Section 1.1 Lines (pp. 1–9) 2. Dx5212(23)52
Dy52222524
Quick Review 1.1 3. Dx5282(23)525
1. y52214(323)52214(0)52210522 Dy512150
2. 3 5322(x11) 4. Dx502050
3 5322x22 Dy52224526
2x 522 5. (a,c)
y
x 521
5
3. m5}22}35}2}1521
524 1
B
4. m5}22(}23)5}5} x
32(21) 4 5
A
5. (a) 3(2)241}1}205
4
621 55 Yes
(b) 3(3)24(21) 05 (b) m5}12(}22)5}3}53
13 (cid:222)5 No 221 1
6. (a) 7 022(21)15 6. (a,c) y
752 15 Yes 5
(b) 1522(22)15
1(cid:222)9 No
7. d 5ˇ(wxw2wwxw)2w1ww(yww2wyw)2w 5 x
2 1 2 1
A
5ˇ(w0w2w1)w2w1w(1ww2w0)w2 B
5ˇ2w
8. d = ˇ(wxw2wwxw)2w1ww(yww2wyw)2w (b) m5}21222(}2(221))5}23}152}13}
2 1 2 1
5!(§1§2§2)§2§1§12§}§1}§2§12§2 7. (a,c) y
3
5
5!(§21§)§2§1§12§}§4}2§2
3
!§§§§ B A
5 11}16}
9 x
5!}§25}§ 5
9
5}5}
3
9. 4x23y57 (b) m5}32}3 5}0}50
2122 23
23y524x17
8. (a,c)
y
y5}4}x2}7} 5
3 3
10. 22x15y523 A
5y52x23 5 x
y5}2}x2}3}
5 5 B
2 Section 1.1
8. continued 26. The line contains (0,0) and (5,2).
(b) m5}21322}125}20}5 (undefined) m5}2522}005}25}
This line has no slope. y5}2}x
5
9. (a) x52
(b) y53 27. 3x14y512
10. (a) x521
4y523x112
(b) y5}4}
11. (a) x503 y52}3}x13
4
(b) y52ˇ2w (a) Slope:2}3}
12. (a) x52p (b) y-intercep4t:3
(b) y50 (c)
13. y51(x21)11
14. y521[x2(21)]11
y521(x11)11
15. y52(x20)13
[210,10] by [210,10]
16. y522[x2(24)]10
y522(x14)10 28. x1y52
y52x12
17. m5}32}05}3} (a) Slope:21
220 2
y5}3}(x20)10 (b) y-intercept:2
2 (c)
y5}3}x
2
2y53x
3x22y50
[210,10] by [210,10]
18. m5}12}15}0}50
221 1 29. }x}1}y}51
y50(x21)11 3 4
}y}52}x}11
y51 4 3
y52}4}x14
19. m5}22}20 5}2}2 (undefined) 3
222(22) 0
Vertical line:x522 (a) Slope:2}4}
3
(b) y-intercept:4
20. m5}22}21 5}2}352}3}
22(22) 4 4 (c)
y52}3}[x2(22)]11
4
4y523(x12)14
4y523x22
[210,10] by [210,10]
3x14y522 30. y52x14
(a) Slope:2
21. y53x22
(b) y-intercept:4
22. y521x12 ory52x12
(c)
23. y52}1}x23
2
24. y5}1}x21
3
[210,10] by [210,10]
25. The line contains (0,0) and (10,25).
m5}252}05}25}5}5}
1020 10 2
y5}5}x
2
Section 1.1 3
31. (a) The desired line has slope 21 and passes through 39. (a) y50.680x19.013
(0,0):
y521(x20)10 or y52x. (b) The slope is 0.68. It represents the approximate average
(b) The desired line has slope }2}151 and passes through weight gain in pounds per month.
(0,0): 21 (c)
y51(x20)10 or y5x.
32. (a) The given equation is equivalent to y522x14.
The desired line has slope 22 and passes through
(22,2):
y522(x12)12 or y522x22. [15,45] by [15,45]
(d) When x530,y <0.680(30)19.013529.413.
(b) The desired line has slope }2}15}1}and passes through She weighs about 29 pounds.
22 2
(22,2): 40. (a) y51,060.4233x22,077,548.669
(b) The slope is 1,060.4233. It represents the approximate
y5}1}(x12)12 or y5}1}x13. rate of increase in earnings in dollars per year.
2 2
(c)
33. (a) The given line is vertical,so we seek a vertical line
through (22,4):x522.
(b) We seek a horizontal line through (22,4):y54.
34. (a) The given line is horizontal,so we seek a horizontal
[1975,1995] by [20,000,35,000]
line through 121,}1}2:y5}1}. (d) When x52000,
2 2
(b) We seek a vertical line through 121,}1}2:x521. y <1,060.4233(2000)22,077,548.669 <43,298.
2 In 2000,the construction workers’average annual com-
35. m5}92}25}7} pensation will be about $43,298.
321 2 41. y51 ?(x23)14
f(x)5}7}(x21)125}7}x2}3} y5x2314
2 2 2 y5x11
Check:f(5)5}7}(5)2}3}516,as expected. This is the same as the equation obtained in Example 5.
2 2
Since f(x)5}72}x2}32},we have m5}72}and b52}32}. 42. (a) When y50,we have }x}51,so x5c.
c
36. m5}24422}(221)5}22}352}32} When x50,we have }dy}51,so y5d.
f(x)52}3}(x22)1(21)52}3}x12 (b) When y50,we have }x}52,so x52c.
2 2 c
Check:f(6)52}3}(6)12527,as expected. When x50,we have }y}52,so y52d.
2 d
Since f(x)52}3}x12,we have m52}3}and b52. The x-intercept is 2cand the y-intercept is 2d.
2 2
37. 2}2} 5}y2}3 43. (a) The given equations are equivalent to y52}2k}x1}3k}
3 42(22) and y52x11,respectively,so the slopes are
2}23}(6) 5y23 2}2}and 21. The lines are parallel when2}2}521,
k k
24 5y23 so k52.
21 5y (b) kTh5e 2lin2e.s are perpendicular when 2}2k}5}22}11,so
38. 2 5}2x22((}2282)) 44. (a) m <}680.242}690.55}201.}4.5523.75 degrees/inch
2(x18) 54 (b) m <}102}685}25}8 <216.1 degrees/inch
420.4 3.6
x18 52 (c) m <}52}10 5}2}5527.1 degrees/inch
x 526 4.724 0.7
(d) Best insulator:Fiberglass insulation
Poorest insulator:Gypsum wallboard
The best insulator will have the largest temperature
change per inch,because that will allow larger
temperature differences on opposite sides of thinner
layers.
4 Section 1.1
45. Slope: k 5}D}p5}10.94}215}9.9}4 y
Dd 10020 100
50.0994 atmospheres per meter 6
At 50 meters,the pressure is (–1, 4)
p50.0994(50)1155.97 atmospheres. (2, 3)
46. (a) d(t)545t
(–1, 1)
(b)
x
(2, 0) 6
y
[0,6] by [250,300] 6
(c) The slope is 45,which is the speed in miles per hour.
(d) Suppose the car has been traveling 45 mph for several
(2, 3)
hours when it is first observed at point Pat time t50.
(e) The car starts at time t50 at a point 30 miles past P. (–1, 1)
x
47. (a) y55632x211,080,280 (2, 0) 6
(b) The rate at which the median price is increasing in (–1, –2)
dollars per year
(c) y52732x25,362,360 50.
y
(d) The median price is increasing at a rate of about $5632
per year in the Northeast,and about $2732 per year in
the Midwest. It is increasing more rapidly in the W (c, d)
(a, b)
Northeast.
x
48. (a) Suppose x8F is the same as x8C. Z X
x5}9}x132
5 (g, h) (e, f)
112}9}2x532 Y
5
2}4}x532
5 Suppose that the vertices of the given quadrilateral are
x5240
(a,b),(c,d),(e,f),and (g,h). Then the midpoints of the
Yes,2408F is the same as 2408C. 1a1c b1d2 1c1e d1f2
consecutive sides are W }},}} ,X }},}} ,
2 2 2 2
(b) Y1}e1}g,}f1}h2,and Z1}g1}a,}h1}b2. When these four
2 2 2 2
points are connected,the slopes of the sides of the resulting
figure are:
[290,90] by [260,60] }d1}f2}b1}d
It is related because all three lines pass through the WX:}2 }2 5}f2}b
point (240,240) where the Fahrenheit and Celsius }c1}e2}a1}c e2a
temperatures are the same. 2 2
}f1}h2}d1}f
49. The coordinates of the three missing vertices are (5,2), XY:}2 }2 5}h2}d
(21,4) and (21,22),as shown below. }e1}g2}c1}e g2c
2 2
y }f1}h2}h1}b
6 ZY:}2 }2 5}f2}b
}e1}g2}g1}a e2a
2 2
(2, 3) }h1}b2}b1}d
(5, 2) WZ:}2 }2 5}h2}d
(–1, 1) }g1}a2}a1}c g2c
2 2
x Opposite sides have the same slope and are parallel.
(2, 0) 6
Section 1.1 5
51. The radius through (3,4) has slope }42}05}4}.
320 3
The tangent line is tangent to this radius,so its slope is }2}152}3}. We seek the line of slope 2}3}that passes through (3,4).
4/3 4 4
y52}3}(x23)14
4
y52}3}x1}9}14
4 4
y52}3}x1}25}
4 4
52. (a) The equation for line Lcan be written as
y52}A}x1}C},so its slope is 2}A}. The perpendicular line has slope }2}1 5}B}and passes through (a,b),so its equation is
B B B 2A/B A
y5}B}(x2a)1b.
A
(b) Substituting }B}(x2a)1bfor yin the equation for line Lgives:
A
Ax1B3}B}(x2a)1b4 5C
A
A2x1B2(x2a)1ABb 5AC
(A21B2)x 5B2a1AC2ABb
x 5}B2a1AC}2ABb
A21B2
Substituting the expression for xin the equation for line Lgives:
A1}B2a1AC}2ABb21By5C
A21B2
By5}2A(B2a}1AC2}ABb) 1}C(A21}B2)
A21B2 A21B2
By5}2AB2a2}A2C1A}2Bb1A2}C1B2C
A21B2
By5}A2Bb1}B2C2}AB2a
A21B2
y5}A2b1BC}2ABa
A21B2
1B2a1AC2ABb A2b1BC2ABa2
The coordinates of Qare }},}} .
A21B2 A21B2
(c) Distance5ˇ(wxw2wa)w2w1w(yw2wwb)w2
5!1§}B2§a§1§A§C}§2§A§B§b§§2§a2§2§1§1}§A2§b§1§B§C}§2§A§B§a§§2§b2§2
A21B2 A21B2
5!1§§}B2a1A}C2AB§}b2a(A}21B2)2§2§1§1§}A2b1B}C2AB§}a2b(A}21B2)2§2
A21B2 A21B2
5!1§}AC§§2§§A§B}b§2§§A2§a2§2§1§1}§BC§§2§§A§B}a§2§§B2§b2§2
A21B2 A21B2
5!1§}A(§C§2§B§}b§2§§Aa§)2§2§1§1}§B(§C§2§A§}a§2§§Bb§)2§2
A21B2 A21B2
5!§}A2(C2A§}a2Bb)2§1§§}B2(C2A§}a2Bb)2
(A21B2)2 (A21B2)2
5!§}(A21B2})(C2§Aa}2Bb)2
(A21B2)2
5!}§(C§2§§A§a}§2§Bb§)§2
A21B2
5})C2Aa}2Bb)
ˇAw2w1wwB2w
5})Aa1B}b2C)
ˇwA2w1wwB2w
6 Section 1.2
n Section 1.2 Functions and Graphs 5. x2,16
(pp. 9–19) Solutions to x2516:x524,x54
Test x526 (26)2536 .16
x2,16 is false when x ,24
Exploration 1 Composing Functions
Test x50: 0250 ,16
1. y35g+f,y45f+g x2,16 is true when 24 ,x ,4
2. Domain of y :[22,2] Range of y :[0,2] Test x56: 62536 .16
3 3
y : x2,16 is false when x .4.
1
Solution set:(24,4)
6. 92x2$0
Solutions to 92x250:x523,x53
Test x524: 92(24)259216527 ,0
[24.7,4.7] by [22,4.2] 92x2$0 is false when x ,23.
y : Test x50: 920259 .0
2 92x2$0 is true when 23 ,x ,3.
Test x54: 924259216527, 0
92x2$0 is false when x .3.
Solution set:[23,3]
[24.7,4.7] by [22,4.2] 7. Translate the graph of f 2 units left and 3 units downward.
y : 8. Translate the graph of f 5 units right and 2 units upward.
3
9. (a) f(x) 54
x225 54
x229 50
(x13)(x23)50
[24.7,4.7] by [22,4.2] x 523 or x53
3. Domain of y :[0,‘); Range of y :(2‘,4] (b) f(x) 526
y : 4 4 x2 25526
4 x2 521
No real solution
10. (a) f(x) 525
[22,6] by [22,6] }1} 525
4. y 5y (y (x))5ˇyw(wx)w5ˇ4ww2wx2w x
y35y2(y1(x))5421(y (x))2542(ˇxw)2542x,x $0 x 52}1}
4 1 2 2 5
(b) f(x) = 0
Quick Review 1.2
1. 3x21#5x13 }1} 50
x
22x#4
No solution
x$22
Solution:[22,‘) 11. (a) f(x) = 4
2. x(x22) .0 ˇxw1ww7 54
Solutions to x(x22)50:x50,x52 x17 516
Test x521: 21(2122)53 .0 x 59
x(x22) .0 is true when x ,0. Check:ˇ9ww1w75ˇ1w6w54; it checks.
Test x51: 1(122)521 ,0
x(x22) .0 is false when 0 ,x ,2. (b) f(x) 51
Test x53: 3(322)53 .0 ˇxw1ww7 51
x(x22) .0 is true when x .2. x17 51
Solution set:(2‘,0) <(2,‘) x 526
3. )x23)#4 Check:ˇ2w6ww1w751; it checks.
24 #x23 #4
21 #x #7 12. (a) f(x) 522
Solution set:[21,7] ˇ3xw2ww1 522
4. )x22)$5 x21 528
x22 #25 or x22 $5 x 527
x #23 or x $7 (b) f(x) 53
Solution set:(2‘,23] <[7,‘) ˇ3xw2ww1 53
x21 527
x 528
Section 1.2 7
Section 1.2 Exercises 8. (a) Since we require 2x $0,the domain is (2‘,0].
1. Since A5pr25p1}d}22,the formula is A5}pd}2,where A (b) (2‘,0]
2 4 (c)
represents area and drepresents diameter.
2. Let hrepresent height and let srepresent side length.
h211}s}225s2 [210,3] by [24,2]
2
h25s22}1}s2 (d) None
4 9. (a) Since we require 32x $0,the domain is (2‘,3].
h25}3}s2 (b) [0,‘)
4
ˇw
h56}}3s (c)
2
Since side length and height must be positive,the formula
ˇw
is h5}}3s.
2
[24.7,4.7] by [26,6]
(d) None
10. (a) Since we require x22(cid:222)0,the domain is
s s (2‘,2) <(2,‘).
h
1
(b) Since }}can assume any value except 0,the range is
s s x22
2 2
s (2‘,0) <(0,‘).
3. S56e2,where Srepresents surface area and erepresents
(c)
edge length.
4. V5}4}pr3,where Vrepresents volume and rrepresents
3
radius.
5. (a) (2‘,‘) or all real numbers
(b) (2‘,4] [24.7,4.7] by [26,6]
(c) (d) None
11. (a) (2‘,‘) or all real numbers
(b) (2‘,‘) or all real numbers
(c)
[25,5] by [210,10]
(d) Symmetric about y-axis (even)
6. (a) (2‘,‘) or all real numbers
(b) [29,‘) [26,6] by [23,3]
(c) (d) None
12. (a) (2‘,‘) or all real numbers
(b) The maximum function value is attained at the point
(0,1),so the range is (2‘,1].
(c)
[25,5] by [210,10]
(d) Symmetric about the y-axis (even)
7. (a) Since we require x21 $0,the domain is [1,‘).
(b) [2,‘)
[26,6] by [23,3]
(c)
(d) Symmetric about the y-axis (even)
[23,10] by [23,10]
(d) None
8 Section 1.2
13. (a) Since we require 2x $0,the domain is (2‘,0]. 18. (a) This function is equivalent to y5ˇxw3,so its domain is
(b) [0,‘) [0,‘).
(c) (b) [0,‘)
(c)
[210,3] by [21,2]
(d) None [22,5] by [22,8]
14. (a) Since we require x(cid:222)0,the domain is (d) None
(2‘,0) <(0,‘). 19. Even,since the function is an even power of x.
(b) Note that }1}can assume any value except 0,so 11}1} 20. Neither,since the function is a sum of even and odd powers
x x of x.
can assume any value except 1. 21. Neither,since the function is a sum of even and odd powers
The range is (2‘,1) <(1,‘). of x(x112x0).
(c) 22. Even,since the function is a sum of even powers of x
(x223x0).
23. Even,since the function involves only even powers of x.
24. Odd,since the function is a sum of odd powers of x.
25. Odd,since the function is a quotient of an odd function (x3)
[24,4] by [24,4] and an even function (x221).
(d) None 26. Neither,since,(for example),y(22)541/3and y(2)50.
15. (a) Since we require 42x2$0,the domain is [22,2]. 27. Neither,since,(for example),y(21) is defined and y(1) is
(b) Since 42x2will be between 0 and 4,inclusive (for x undefined.
in the domain),its square root is between 0 and
28. Even,since the function involves only even powers of x.
2,inclusive. The range is [0,2].
29. (a)
(c)
[29.4,9.4] by [26.2,6.2]
[24.7,4.7] by [23.1,3.1]
Note that f(x)52)x23)12,so its graph is the graph
(d) Symmetric about the y-axis (even)
of the absolute value function reflected across the
16. (a) This function is equivalent to y5ˇ3xw2,so its domain is x-axis and then shifted 3 units right and 2 units upward.
all real numbers. (b) (2‘,‘)
(b) [0,‘) (c) (2‘,2]
(c)
30. (a) The graph of f(x) is the graph of the absolute value
function stretched vertically by a factor of 2 and then
shifted 4 units to the left and 3 units downward.
[22,2] by [21,2]
(d) Symmetric about the y-axis (even)
17. (a) Since we require x2(cid:222)0,the domain is
(2‘,0) <(0,‘) [210,5] by [25,10]
(b) (2‘,‘) or all real numbers
(b) Since }x1}2 .0 for all x,the range is (1,‘). (c) [23,‘)
(c) 31. (a)
[24,4] by [21,5] [24.7,4.7] by [21,6]
(d) Symmetric about the y-axis (even) (b) (2‘,‘) or all real numbers
(c) [2,‘)
Section 1.2 9
32. (a) 44. Line through (21,0) and (0,23):
m5}23}20 5}2}3523,so y523x23
02(21) 1
Line through (0,3) and (2,21):
[24,4] by [22,3] m5}212}35}2}4522,soy522x13
220 2
(b) (2‘,‘) or all real numbers h
23x23, 21 ,x #0
(c) [0,‘) f(x)5 22x13, 0 ,x #2
33. (a)
45. Line through (21,1) and (0,0):y52x
Line through (0,1) and (1,1):y51
Line through (1,1) and (3,0):
(b) ([22‘3.,7‘,5). 7o]r bayl l[ 2re4a,l 9n]umbers m5}0322}115}22}152}12},
(c) (2‘,‘) or all real numbers soy52}1}(x21)1152}1}x1}3}
h 2 2 2
34. (a) 2x, 21 #x ,0
f(x)5 1, 0 ,x #1
2}1}x1}3}, 1 ,x ,3
2 2
[22.35,2.35] by [21,3] 46. Line through (22,21) and (0,0):y5}1}x
(b) (2‘,‘) or all real numbers 2
(c) [0,‘) Line through (0,2) and (1,0):y522x12
35. Because if the vertical line test holds,then for each Line thhrough (1,21) and (3,21):y521
x-coordinate,there is at most one y-coordinate giving a
point on the curve. This y-coordinate would correspond to }1}x, 22 #x #0
2
the value assigned to the x-coordinate. Since there is only f(x)5 22x12, 0 ,x #1
one y-coordinate,the assignment would be unique.
36. If the curve is not y50,there must be a point (x,y) on the 21, 1 ,x #3
curve where y(cid:222)0. That would mean that (x,y) and (x,2y) 1T 2
47. Line through }},0 and (T,1):
are two different points on the curve and it is not the graph
2
of a function,since it fails the vertical line test. m5}12}0 5}2},soy5}2}1x2}T}2105}2}x21
37. No T2h (T/2) T T 2 T
38. Yes 0, 0 #x #}T}
39. Yes f(x)5 }2}x21, }T},x #T2
40. No hT 2
41. Line through (0,0) and (1,1):y5x
Line through (1,1) and (2,0):y52x12 A, 0 #x ,}T}
2
h
x, 0 #x #1 2A, }T}#x ,T
f(x)5 2x12, 1 ,x #2 48. f(x)5 2
A, T #x ,}3T}
h 2
2, 0 #x ,1 2A, }3T}#x #2T
2
0, 1 #x ,2
42. f(x)5 2, 2 #x ,3 49. (a) f(g(x))5(x223)155x212
0, 3 #x #4 (b) g(f(x))5(x15)223
5(x2110x125)23
43. Line through (0,2) and (2,0):y52x12 5x2110x122
(c) f(g(0))5021252
Line through (2,1) and (5,0):m5}0522}125}23}152}13}, (d) g(f(0))502110?0122522
so y52}1}(x22)1152}1}x1}5} (e) g(g(22))5[(22)223]22351223522
h 3 3 3
2x12, 0 ,x #2 (f) f(f(x))5(x15)155x110
f(x)5
2}1}x1}5}, 2 ,x #5
3 3
10 Section 1.2
50. (a) f(g(x))5(x21)115x g +f:
(b) g(f(x))5(x11)215x
(c) f(g(x))50
(d) g(f(0))50
(e) g(g(22))5(2221)2152321524
(f) f(f(x))5(x11)115x12 [24.7,4.7] by [22,4]
51. (a) Enter y 5f(x)5x27,y 5g(x)5ˇxw, Domain:(2‘,21] <[1,‘)
y 5(f1+g)(x)5y (y (x)),2 Range:[0,‘)
3 1 2
and y 5(g+f)(x)5y (y (x)) (b) (f +g)(x)5(ˇxw1ww2)223
4 2 1
f +g: g +f: 5(x12)23,x $22
5x21,x $22
(g +f)(x)5ˇ(wx2w2ww3)w1ww25ˇxw2w2w1
54. (a) Enter y (x)5f(x)5}2x2}1,y 5}3x1}1,
1 x13 2 22x
y 5(f +g)(x)5y (y (x)),
3 1 2
[210,70] by [210,3] [23,20] by [24,4] and y 5(g +f)(x)5y (y (x)).
4 2 1
Domain:[0,‘) Domain:[7,‘) Use a “decimal window”such as the one shown.
Range:[27,‘) Range:[0,‘) f +g:
(b) (f +g)(x)5ˇxw27 (g +f)(x)5ˇxw2ww7
52. (a) Enter y 5f(x)512x2,y 5g(x)5ˇxw,
1 2
y 5(f +g)(x)5y (y (x)),
3 1 2
and y 5(g +f)(x)5y (y (x))
4 2 1
f +g:
[29.4,9.4] by [26.2,6.2]
Domain:(2‘,2) <(2,‘)
Range:(2‘,2) <(2,‘)
g +f:
[26,6] by [24,4]
Domain:[0,‘)
Range:(2‘,1]
g +f:
[29.4,9.4] by [26.2,6.2]
Domain:(2‘,23) <(23,‘)
Range:(2‘,23) <(23,‘)
21}3x1}1221
[22.35,2.35] by [21,2.1] (b) (f +g)(x)5}22x}
Domain:[21,1] }3x1}113
22x
Range:[0,1] 5}2(3x1}1)2(}22x),x(cid:222)2
(b) (f +g)(x)512(ˇxw)2512x,x $0 (3x11)13(22x)
(g +f)(x)5ˇ1ww2wx2w
5}7}x,x(cid:222)2
53. (a) Enter y 5f(x)5x223,y 5g(x)5ˇxw1ww2, 7
1 2
y 5(f +g)(x)5y (y (x)), 5x,x(cid:222)2
3 1 2
and y 5(g +f)(x)5y (y (x)).
4 2 1
f +g: 31}2x2}1211
(g +f)(x)5}x13}
22}2x2}1
x13
5}3(2x2}1)1(}x13),x(cid:222)23
2(x13)2(2x21)
[210,10] by [210,10] 5}7}x,x(cid:222)23
7
Domain:[22,‘) 5x,x(cid:222)23
Range:[23,‘)
