x
y
y
Chapter 7 Summary and Review: Review Exercises 189
3. g(x)=−2x+5
4. f(x)=3x2−2x+7
5. C(t) = 309.2t+ 3717.7
6. y=−3x+2
We find some ordered pairs that are solutions, plot them,
and draw and label the line.
7. y=5
2x−3
4 7 (4,7)
8. y=|x−3|
x y
3 0
−3 6
then determine y. For example, if x= 2, then 3 −22=
3−4=−1. We find several ordered pairs, plot them, and
connect them with a smooth curve.
x y
12. a) Locate 2 on the horizontal axis and then find the
point on the graph for which 2 is the first coordinate.
13. f(x)= 5
x−4
x−4=0
x= 4 Adding 4 on both sides
x
(2, 0)
14. g(x)=x−x2
15. f(x)=−3x+2
16. First we find the slope-intercept form of the equation by
solving for y. This allows us to determine the slope and
y-intercept easily.
18. 2y+x=4
To find the x-intercept we let y= 0 and solve for x.
We plot these points and draw the line.
19. 2y=6−3x
2·0=6−3x
The x-intercept is (2,0).
To find the y-intercept we let x= 0 and solve for y.
20. g(x)=−2
3x−4
First we plot the y-intercept (0,−4). We can think of the
x 3
y
x
Chapter 7 Summary and Review: Review Exercises 191
21. f(x)=5
slope 5
2. Starting at the y-intercept and using the slope,
we find another point by moving 5 units up and 2 units to
23. f(x)=4
Since xis missing, all ordered pairs (x, 4) are solutions.
The graph is parallel to the x-axis.
24. We first solve each equation for yand determine the slope
The slopes are not the same, so the lines are not parallel.
25. We first solve each equation for yand determine the slope
of each line.
26. We first solve each equation for yand determine the slope
of each line.
2x+8y=5
The slopes are the same and the y-intercepts are different,
so the lines are parallel.
27. x= 4 is a vertical line and y=−3 is a horizontal line, so
28. We use the slope-intercept equation and substitute 4.7 for
mand −23 for b..
29. Using the point-slope equation:
y−(−5) = −3(x−3)
192 Chapter 7: Graphs, Functions, and Applications
30. First find the slope of the line:
x1, 3 for y1, and −3
2for m.
y−y1=m(x−x1)
y=−3
2x
Using the slope-intercept equation:
31. First solve the equation for yand determine the slope of
the given line.
Substitute 14 for x1,−1 for y1, and −5
7for m.
9=b
32. First solve the equation for yand determine the slope of
the given line.
3.
Using the point-slope equation:
Substitute 5 for x1, 2 for y1, and 1
3for m.
2=1
3·5+b
33. a) We form pairs of the type (x, R) where xis the
Chapter 7 Test 193
First we find the slope:
m=43.94 −44.66
40 −0=−0.72
40 =−0.018.
Using the slope and the y-intercept, (0,44.66)
b) 2000 is 28 years after 1972, so to estimate the record
in 2000, we find R(28):
2010 is 38 years after 1972, so to estimate the record
6x+y=−11
Answer A is correct.
36. The cost of xjars of preserves is $2.49x, and the ship-
ping charges are $3.75+$0.60x. Then the total cost is
Chapter 7 Discussion and Writing Exercises
1. A line’s x– and y-intercepts are the same only when the
2. The concept of slope is useful in describing how a line
3. Find the slope-intercept form of the equation.
4. For R(t)=50t+ 35, m= 50 and b= 35; 50 signifies that
6. Using algebra, we find that the slope-intercept form of
Chapter 7 Test
1. Yes; each member of the domain is matched to only one
member of the range.
x
y
y
194 Chapter 7: Graphs, Functions, and Applications
4. g(x)=x2+7
5. h(x)=−6
6. f(x)=|x+7|
7. y=−2x−5
8. f(x)=−3
5x
5−3
9. g(x)=2−|x|
We find some function values, plot the corresponding
points, and draw the graph.
x g(x)
−2 0
points, and draw the graph.
2 5
12. 2x=−4
Chapter 7 Test 195
13. a) In 2005, x= 2005 −1990 = 15. We find A(15).
15. It is possible for a vertical line to intersect the graph more
16. f(x)= 8
2x+3
2x=−3
x=−3
2
18. a) Locate 1 on the horizontal axis and then find the point
19. f(x)=−3
20. First we find the slope-intercept form of the equation by
solving for y. This allows us to determine the slope and
23. We can use the coordinates of any two points on the graph.
We’ll use (10,0) and (25,12).
24. 2x+3y=6
To find the x-intercept we let y= 0 and solve for x.
2·0+3y=6
3y=6
We use a third point as a check. We choose x=−3 and
y
25. f(x)=−2
3x−1
the points and draw the line.
26. We first solve each equation for yand determine the slope
27. The slope of y=−2x+5 is−2.
We solve the second equation for yand determine the
28. We use the slope-intercept equation and substitute −3 for
29. y=f(x)=mx +b
30. Using the point-slope equation:
Substitute 1 for x1,−2 for y1, and −4 for m.
y=mx +b
−2=−4·1+b
31. First find the slope of the line:
m=−6−15
4−(−10) =−21
14 =−3
2
y=mx +b
−6=−3
2·4+b
x−2y= 5 Given line
The slope of the given line is 1
Cumulative Review Chapters 1 – 7 197
Using the point-slope equation:
−1=1
2(4) + b
−1=2+b
33. First solve the equation for yand determine the slope of
y−5=3(x−2)
y−5=3x−6
y=3x−1
Using the slope-intercept equation:
5=6+b
34. a) Note that 2010 −1970 = 40. Thus, the data points
35. Using the point-slope equation, y−y1=m(x−x1), with
36. First solve each equation for yand determine the slopes.
3x+ky =17
−5y=−8x+26
Cumulative Review Chapters 1 – 7
1. −2[1.4−(−0.8−1.2)] = −2[1.4−(−2)]
2. (1.3×108)(2.4×10−10)
198 Chapter 7: Graphs, Functions, and Applications
5. x2−9
6. t2−16
(t+4)
2=(t+ 4)(t−4)
(t+ 4)(t+4)
2
x−1
x+2
=x3+2x2−x2
2x+4−x=x3+x2
x+4
=x2(x+1)
x+4
8. (1 −3x2)(2 −4x2)=2−4x2−6x2+12x4=
11. −2x2(x−2x2+3x3)
=−2x2·x−2x2(−2x2)−2x2·3x3
14. (−8y2−y+2)−(y3−6y2+y−5)
2x3−x2
−2x2−x
16. 7
5x−25 +x+7
5−x=7
5(x−5) +x+7
5−x
17. 2x−1
x−2−2x
2−x=2x−1
x−2−2x
2−x·−1
−1
=2x−1
x−2−−2x
x−2
=4x−1
x−2
18. y2+y
Cumulative Review Chapters 1 – 7 199
19. 7x+7
x2−2x÷14
3x−6=7x+7
x2−2x·3x−6
14
2x
24. 3m3+6m2−45m=3m(m2+2m−15) =
x=−9
28. 5x+3≥6(x−4)+7
29. 1.5x−2.3x=0.4(x−0.9)
30. 2x2= 338
32. 2
x−3
x−2=1
x,LCM is x(x−2)
33. 1+ 3
x+x
x+1=1
x2+x
2x2+4x+2=0
2(x2+2x+1)=0
34. w−9
10 =−9
10 +w
20 −5y≤45+5y
36. 9x−4−2x=5x−5+2x
37. N=rx −t
r=x
38. Familiarize. Let p= the price of the frame. Then the
total amount paid was p+6% of p,orp+0.06p,or1.06p.
39. Familiarize. Let t= the number of hours required to
roof the house, working together. Then in thr David does
Check.In20
3hr David does 20/3
15 ,or 4
9, of the job and
40. Familiarize. Let l= the length of the second leg of the
144 + l2=l2+16l+64
Check.12
2+5
2=144+25=169=13
2. The answer
41. Familiarize. Let c= the number of defective chips to be
expected in a batch of 1800 chips.
1800 chips.
42. Familiarize. Let b= the base of the triangle, in feet.
y 2
Cumulative Review Chapters 1 – 7 201
Check. The length of the base cannot be negative, so we
check only 4. If b= 4, then b+ 5 = 4 + 5, or 9. The area
43. Familiarize and Translate. We are told we have in-
verse variation between the variables hand b. We write
an equation of inverse variation.
44. y=kx
2.4=k·12
2.4
45. g(x)=−1
2(−6)+6=3+6=9
46. f(x)=|2x−3|
48. 2x+3y=6
49. m=−4−6
2−(−5) =−10
7=−10
7
y=−10
7x+b
6=−10
52. Graph: 2x+5y=10
x=5
5y=10
−10 + 5y=10
202 Chapter 7: Graphs, Functions, and Applications
53. f(x)=−3
54. 2x−y=3
The y-intercept is (0,−3).
We find a third point as a check. Let x=3.
55. x−4=0
The x-intercept is (−1,0).
A third point is (−2,−3). We plot the intercepts and this
point and draw the graph.
57. x2+2<0
58. x−5
x+3−x2−6x+5
x2+x−2÷x2+4x+3
x2+3x+2
59. We write each equation in slope-intercept form.
y−kx =4 10x−3y=−12
y=kx +4 −3y=−10x−12