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Chapter 3 Review
Evaluate each function at the given input values.
3.1
Solve these equations.
13. f ( x) = 2 x2 − 4x + 1
1. 4x2 – 25 = 0
a. f (3)
2. 2x2 + 5x = 12
b. f (h)
3. x2 + 4x – 7 = 0
9
14. g ( p) =
3p + 2
4. 6x2 – 5 = 13x
a. g(0)
5. 2(w – 1)2 – 8 = 0
6. x + 5 =
7.
24
x
2
1
1
−
=
x−5 x+1 4
8. 2(y + 1)2 – 14 = y2 + 5y + 30
b. g(w + 1)
15. h( x) =
a. h(4)
b. h(x2)
16. f ( y ) =
3.2
Indicate whether or not the relation represents a
function. If it is a function, find the domain.
9. 3x2 + 4y 2 = 1
10. y =
2x
( x − 5)(2 x + 1)
2x + 1
x−8
2−y +
y +1
a. f (2)
b. f (y + h)
17. y( x) =
x2 − 4
a. y(3)
b. y(x2 + 1)
11. y = (3 + x2 ) x + 5
12. y =
18
x−4
1
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Chapter 3 Review
3.3
For each parabola, find the following:
(a)
(b)
(c)
(d)
its vertex,
the axis of symmetry,
whether the parabola is concave up or down,
whether the vertex is a maximum or minimum
point,
(e) the x-intercept(s), if any exist,
(f) sketch the graph.
18.
y = 2(x +
19.
y = –(x – 5)2 + 2
20.
y = (x – 2)2 + 1
21. y = −
3)2
–4
1 2 3
x + x+5
2
2
22.
y = –4(x + 1)2 – 1
23.
y = x2 – 6x + 5
24. y =
2 2
x −2
9
25. A farmer wants to fence a rectangular field and
then divide it in half with a fence down the
middle parallel to one side. If 1488 feet of fence
is to be used, what is the maximum area of the
overall lot?
26. If a profit function is given by P(x) = –2x2 +
2320x – 1000, where x represents the number
of motor bikes made and sold, how many motor
bikes need to be sold for maximum profit? What
is the maximum profit?
28. revenue: R( x) = −0.4x2 + 53.6x
cost:
C( x) = 0.4x2 + 12.8x + 496
29. revenue: R( x) = −0.9x2 + 73x
cost:
C( x) = 0.6x2 + 10 x + 588
Given the supply and demand equations, find the
equilibrium quantity and price.
30. supply:
demand:
p = q 2 + 8q + 20
31. supply:
demand:
p = 2(q + 5)2 + 6
p = 100 − 4q − q 2
p = −7(q + 3)2 + 994
32. supply:
5 p − q = 18
demand: pq = 3540 + 19q
33. The supply and demand functions for Margo’s
p
design products are given by q = 2 and pq =
10(20 + 4) respectively. If Margo is taxed $4 per
product and passes that tax on to the consumer
as a price increase, find the market equilibrium
point.
34. The cost of producing Bill’s handiwork is given
by C(x) = 0.4x 2 + 12.8x + 496 and he’s found the
demand for his product obeys the equation
p = –0.4x + 53.6. If he can only produce fewer
than 30 of his handiwork projects per week,
how many must he make and sell to break even?
How much profit will he make if he sells all
30 units?
3.5
For each polynomial function, find/do the following:
3.4
Find the number of units that need to be produced
and sold to break even, given the revenue and cost
functions.
27. revenue: R( x) = 1600 x − x2
cost:
C( x) = 1.6( x − 500)2 + 200000
(a)
(b)
(c)
(d)
(e)
its degree,
all the zeros (roots),
the y-intercept,
the x-intercept(s), if any exist,
sketch the graph.
35. y =
1 3
( x + 2 x2 − 8 x)
5
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Chapter 3 Review
36. y =
3.6
1 2
( x − 2 x − 3)2
8
Analyze each rational function by answering the
following questions.
37. y = −
1
( x + 4)( x2 − 16)
16
38. y = −
1
( x − 2 )2 ( x − 2 )2 − 16
24
(
(a)
(b)
(c)
(d)
(e)
(f)
)
39. y = x5 − 2 x3 + x
What is the domain?
Find the vertical asymptote(s), if there are any.
Find the horizontal asymptote, if it exists.
Find the y-intercept, if it exists.
Find the x-intercept(s), if any exist.
Sketch the graph.
3
x−4
For each piecewise function, fill in the table of
points and then sketch the graph.
43. f ( x) =
3x − 1, x ≥ 0
40. f ( x) =  2
− x + 2, x < 0
44. y =
2x + 1
x
45. y =
x2 − 4
x −x−2
46. y =
x
( x + 2 )( x − 2 )
47. y =
4
x2 − 9
x
–2
–1
0
1
2
3
y
1 2
 x ,x≥2
 2
41. y( x) =  x, −1 ≤ x < 2

−2 x − 2, x < −1

x
–2
–1
0
1
2
3
For each function, answer the following questions,
compared to the base function graph.
3
(a) What is the vertical shift?
(b) What is the horizontal shift?
(c) Is the graph stretched/shrunk vertically? If so,
by what factor?
(d) Is the graph stretched/shrunk horizontally? If
so, by what factor?
(e) Is the graph reflected? If so, is it a vertical or
horizontal reflection?
(f) Sketch the graph.
8, x ≥ 2

42. h( x) =  x3 , −2 ≤ x < 2

−1, x < −2
y
–3
–2
0
1
2
3.7
y
x
3
2
48. y = − x + 1 − 3
49. f ( x) =
50. h( x) =
1
( x + 2 )2 + 5
2
−4( x − 1) + 2
51. g ( x) = − x2 − 6x + 1
52. y = 2( x − 4)3
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Chapter 3 Review
4
3.8
For each pair of given functions, find the following:
(f + g)(x)
(fg)(1)
(f g)(x)
g(f (x))
(g – f )(2)
f
(f) (3)
g
(g) (f f )(x)
(a)
(b)
(c)
(d)
(e)
3
55. f ( x) = x + x
2
g ( x) =
x+1
x+5
x−3
g ( x) = x2
56. f ( x) =
57. f ( x) = 2 x − 6
x
g ( x) = 2
x − 25
53. f ( x) = 2 x + 1
g ( x) = − x + 5
58. f ( x) =
54. f ( x) = x2 + 3
59. f ( x) = −4x
g ( x) = x − 1
x
g ( x) = x − 1
3
g ( x ) = x 2 + 3x
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Chapter 3 Review
CHAPTER 3 REVIEW ANSWER KEY
±5
1. x = 2
3
2. x = –4, 2
3. x = –2 ± 11
5
4. x = – 1
, 3 2
5. w = –1, 3
6. x = 3, –8
7. x = 4 ± 3
5
8. y = –6, 7
9. not a function
1
10. is a function; domain: x ∈, x ≠ 5, – 2
11. is a function; domain: x ∈, x ≥ –5
12. is a function; domain: x ∈, x > 4
13. a. 7
b. 2h2 – 4h + 1
14. a.
9
or
2
19. a.
b.
c.
d.
e.
f.
(5, 2)
x=5
down
maximum
2, 0) and (5 – 2
, 0)
(5 + 20. a.
b.
c.
d.
e.
f.
(2, 1)
x=2
up
minimum
none
9 2
2
9
b.
3w + 5
15. a. – 9
4
b.
2 x2 + 1
x2 − 8
 3 49 
21. a.  , 
2 8 
16. a. 3
b.
2−y−h+
y +h+1
17. a. 5
b.
18. a.
b.
c.
d.
e.
f.
x4 + 2 x2 − 3
(–3, –4)
x = –3
up
minimum
2, 0) and (–3 – 2
, 0)
(–3 + b. x = 3
2
c. down
d. maximum
e. (–2, 0) and (5, 0)
f.
5
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Chapter 3 Review
22. a.
b.
c.
d.
e.
f.
(–1, –1)
x = –1
down
maximum
none
23. a.
b.
c.
d.
e.
f.
(3, –4)
x=3
up
minimum
(1, 0) and (5, 0)
24. a.
b.
c.
d.
e.
f.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
(0, –2)
x=0
up
minimum
(3, 0) and (–3, 0)
372 square feet
580 boxes, $671,800
~231 or 1000 units
20 or 31 units
14 or 28 units
(4, $68)
(7, $294)
(177, $39)
(10, $24)
20; $8
3:57 PM
Page 6
35. a.
b.
c.
d.
e.
3
x = 0, 2, –4
(0, 0)
(0, 0), (2, 0) and (–4, 0)
36. a. 4
b. x = –1, 3
c. 0, 9
8
d. (–1, 0) and (3, 0)
e.
37. a.
b.
c.
d.
e.
3
x = –4, 4
(0, 4)
(4, 0) and (–4, 0)
38. a.
b.
c.
d.
e.
4
x = 2, –2, 6
(0, 2)
(–2, 0), (2, 0) and (6, 0)
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Chapter 3 Review
39. a.
b.
c.
d.
e.
5
x = 0, 1, –1
(0, 0)
(0, 0), (1, 0) and (–1, 0)
43. a.
b.
c.
d.
e.
f.
x ∈, x ≠ 4
x=4
y=0
(0, –0.75)
none
44. a.
b.
c.
d.
e.
f.
x ∈, x ≠ 0
x=0
y=2
none
(–0.5, 0)
45. a.
b.
c.
d.
e.
f.
x ∈, x ≠ 2, –1
x = –1
y=1
(0, 2)
(–2, 0)
46. a.
b.
c.
d.
e.
x ∈, x ≠ ±2
x = 2, x = –2
y=0
(0, 0)
(0, 0)
40.
x
–2
–1
0
1
2
3
y
–2
1
–1
2
5
8
41.
x
–2
–1
0
1
2
3
y
2
–1
0
1
2
4.5
42.
x
–3
–2
0
1
2
3
y
–1
–8
0
1
8
8
7
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Chapter 3 Review
8
f.
47. a. x ∈, x ≠ ±3
b. x = 3, x = –3
c. y = 0
d. 0, – 4
9
e. none
f.
50. a.
b.
c.
d.
e.
f.
up 2
right 1
no
yes; shrunk 4
yes; horizontal
51. a.
b.
c.
d.
e.
f.
up 10
left 3
no
no
yes; vertical
52. a.
b.
c.
d.
e.
f.
none
right 4
yes; stretched 2
no
no
53. a.
2x + 1 − x + 5
48. a.
b.
c.
d.
e.
f.
down 3
left 1
no
no
yes; vertical
49. a.
b.
c.
d.
e.
f.
up 5
left 2
yes; shrunk by half
no
no
b. 4 3
c.
−2 x + 11
d. 5 − 2 x + 1
e. −7 − 5
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Chapter 3 Review
57. a. 2 x − 6 +
f.
7
2
g.
2 2x + 1 + 1
54. a. x2 + x + 2
b. 0
c. x2 − 2 x + 4
d. x2 + 3 − 1 or x2 + 2
55. a. x3 + x +
2
x+1
2x
−6
x2 − 25
d.
2x − 6
4x − 24x + 11
2
2( x2 + 2 x + 5)
( x + 1)3
d. x x − 1
e. 7 − 2
28
3
f. 60
f.
g. x + 3x + 3x + 2 x + x
7
x+5
x−3
b. –3
x2 + 5
x2 − 3
( x + 5)2
( x − 3)2
e. 11
f. DNE
d.
5 − 3x
x−7
x3 − 1
c.
e. −
9
x −1
b. 0
2
d. 3
x + x+1
g.
c.
58. a. x3 +
b. 2
c.
1
6
e.
g. x4 + 6x2 + 12
56. a. x2 +
b.
40
21
f. 0
g. 4x – 18
e. –6
f. 6
c.
x
x − 25
2
5
3
g.
59. a.
b.
c.
d.
e.
3
26
4
x
x2 – x
–16
–4x2 – 12x
16x2 – 12x
18
f. – 2
3
g. 16x
9
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