College Algebra Problems, algebra homework help

the details are in the pictures

EXERCISE SET 2.7
Section 2.7 Inverse Functions 309
Practice Exercises
each pair of functions f and g are inverses of each other.
In Exercises 1-10, find f(g(x)) and g(f(x)) and determine whether
33.
34.
у
х
1. f(x) = 4x and g(x)
2. f(x) = 6x and g(x)
4
X
6
x – 8
3
X – 9
3. f(x) = 3x + 8 and g(x)
4. f(x) = 4x + 9 and g(x)
5. f(x) = 5x – 9 and g(x)
In Exercises 35-38, use the graph off to draw the graph of its
inverse function.
35.
4
x + 5
у
36.
у
4-
9
x + 3
4+
3-
6. f(x) = 3x – 7 and g(x)
7
1
1+
X
3
+4
7. f(x) =
2 3 4
–4-3-2-11
1 2 3 4 5
3
x – 4
2
2
-2-
-3-
-3-2-11-
-2+
-3+
-4-
8. f(x)
x – 5
-1
–
37.
у
38.
y
4
and g(x)
4
2
and g(x) + 5
X
9. f(x) = -x and g(x) = -x
10. f(x) = Vx – 4 and g(x) = x3 + 4
The functions in Exercises 11-28 are all one-to-one. For each function,
a. Find an equation for f-f(x), the inverse function.
b. Verify that your equation is correct by showing that
f-(x)) = x and f-f(f(x)) = x.
11. f(x) = x + 3
12. f(x) = x + 5
13. f(x) = 2x
14. f(x) = 4x
4
3
2
2-
py
х
X
2 3 4
2 3 4
TH
21. f(x)
=
–
X
х
15. f(x) = 2x + 3
16. f(x) = 3x – 1
17. f(x) = x + 2
18. f(x) = x3 – 1
19. f(x) = (x + 2)
20. f(x) = (x – 1))
1
2
22. f(x) =
23. f(x) = Vx
24. f(x) = x
4
25. f(x) = 2 – 3
26. f(x)
+9
2x + 1
2x – 3
28. f(x)
x – 3
Which graphs in Exercises 29–34 represent functions that have
nverse functions?
у
30.
y
х
X
27. f(x)
x + 1
—4-3-2-1
-4-3-2-1
-2-
-2+
-3
-3-
–
-4+
In Exercises 39-52,
a. Find an equation for f-‘(x).
b. Graph f and f-1 in the same rectangular coordinate system.
C. Use interval notation to give the domain and the range of f
and f-1.
39. f(x) = 2x – 1
40. f(x) = 2x – 3
41. f(x) = x2 – 4, x 20 42. f(x) = x2 – 1, x = 0
43. f(x) = (x – 1)*, x = 1
44. f(x) = (x – 1)?, x 2 1
45. f(x) = x3 – 1
46. f(x) = x3 + 1
47. f(x) = (x + 2)
48. f(x) = (x – 2)
(Hint for Exercises 49–52: To solve for a variable involving an nth
root, raise both sides of the equation to the nth power: (Vy)” = y.)
49. f(x) = Vx – 1
50. f(x) = 7x + 2
51. f(x) = x + 1
52. f(x) = x – 1
Practice Plus
In Exercises 53-58, f and g are defined by the following tables.
Use the tables to evaluate each composite function.
f(x)
g(x)
53. f(g(1))
54. f(g(4)
-1
1
–1
55. (gºf)(-1)
0 4
1 1
56. (8 80
1 5
4 2
57. f-‘(g(10)
2 -1
10 -1 58. f-‘(g(1))
9
0
у
32
.
у
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Homework – Week 4
Due – Monday, April 10, 2017
Section
Assignment
2.7: pg. 309
6, 16, 18, 26, 30, 36, 40, 42, 46
3.1: p. 343
10, 14, 22, 28, 36, 42, 44, 46, 50,
54, 58
Section 3.1 Quadratic Functions 343
f(x) = 4×2 – 16x + 300 is f(2).
3. True or false: The y-coordinate of the vertex of
6. The difference between two numbers is 8. If one
number is represented by x, the other number can be
P(x), expressed in the form P(x) = ax’ + bx + c, is
expressed as
7. The perimeter of a rectangle is 80 feet. If the length
of the rectangle is represented by x, its width can
be expressed as
The area of the rectangle,
A(x), expressed in the form A(x) = ax2 + bx + c, is
A(x)
The product of the numbers,
P(x) =
EXERCISE SET 3.1
Practice Exercises
7.
у
8.
у
In Exercises 1-4, the graph of a quadratic function is given. Write
the function’s equation, selecting from the following options.
HP
3
f(x) = (x + 1)2 – 1
h(x) = (x – 1)2 + 1
g(x) = (x + 1)2 + 1
j(x) = (x – 1)2 – 1
4-
3
2
1
1
X
1.
2.
4-3-2-11
1 2 3 4
4-3-2-11+ 1 2 3 4
-2
-3-
-4
THAI
3
2
UV
1
2 3 4
X
4-3-2-11
-2
1 2 3 4
-4-3-2-11-
-2
1-24
In Exercises 9–16, find the coordinates of the vertex for the
parabola defined by the given quadratic function.
9. f(x) = 2(x – 3)2 + 1 10. f(x) = -3(x – 2)2 + 12
11. f(x) = -2(x + 1)2 + 5 12. f(x) = -2(x + 4)2 – 8
13. f(x) = 2×2 – 8x + 3 14. f(x) = 3×2 – 12x + 1
15. f(x) = -x2 – 2x + 8 16. f(x) = -2x² + 8x – 1
3.
у
4.
y
6-
5
4-
3
6
5
4
3
2-
1
х
X
4-3-2-117
2 3 4
1 2
ܗܝܙ
–4-3-2-
-27
In Exercises 17–38, use the vertex and intercepts to sketch
the graph of each quadratic function. Give the equation of the
parabola’s axis of symmetry. Use the graph to determine the
function’s domain and range.
17. f(x) = (x – 4)2 – 1 18. f(x) = (x – 1)2 – 2
19. f(x) = (x – 1)2 + 2 20. f(x) = (x – 3)2 + 2
21. y – 1 = (x – 3)? 22. y – 3 = (x – 1)2
23. f(x) = 2(x + 2)2 – 1 24. f(x) = – (x – 2)2
25. f(x) = 4 – (x – 1)2 26. f(x) = 1 – (x – 3)2
27. f(x) = x2 – 2x – 3 28. f(x) = x2 – 2x – 15
29. f(x) = x2 + 3x – 10 30. f(x) = 2×2 – 7x – 4
31. f(x) = 2x – x2 + 3
32. f(x) = 5 – 4x – x2
33. f(x) = x2 + 6x + 3 34. f(x) = x2 + 4x – 1
35. f(x) = 2×2 + 4x – 3 36. f(x) = 3×2 – 2x – 4
37. f(x) = 2x – x2 – 2 38. f(x) = 6 – 4x + x2
–2+
In Exercises 5-8, the graph of a quadratic function is given. Write
the function’s equation, selecting from the following options.
f(x) = x2 + 2x + 1
h(x) = x2 – 1
8(x) = x2 – 2x + 1
j(x) = -x2 – 1
6.
S,
у
3-
24
1
3-
2-
1
X
In Exercises 39-44, an equation of a quadratic function is given.
a. Determine, without graphing, whether the function has a
minimum value or a maximum value.
b. Find the minimum or maximum value and determine
where it occurs.
c Identify the function’s domain and its range.
39. f(x) = 3×2 – 12x – 1
41. f(x) = -4x² + 8x – 3 42. f(x) = -2×2 – 12x + 3
43. f(x) = 5×2 – 5x
44. f(x) = 6×2 – 6x
4-3-2-114 12.
1 2 3 4
-2+
-3
1 2 3 4
-2+
-3+
40. f(x) = 2×2 – 8x – 3
344 Chapter 3 Polynomial and Rational Functions
66. I
feet, can be modeled by
g(x) = -0.04×2 + 2.1x + 6.1,
b
fi
a
verify your answers using the red graph.
previous column is released at an angle of 65°, its height, g(x).
58. When the shot whose path is shown by the red graph in the
where x is the shot’s horizontal distance, in feet, from its porn
of release. Use this model to solve parts (a) through C) and
foot, of the shot and how far from its point of release dos
a. What is the maximum height, to the nearest tenth of a
nearest tenth of a foot, or the distance of the throw?
b. What is the shot’s maximum horizontal distance, to the
The height of the ball, f(x), in feet, can be modeled by
59. A ball is thrown upward and outward from a height of 6 feet
this occur?
Practice Plus
In Exercises 45-48, give the domain and the range of each
quadratic function whose graph is described.
45. The vertex is (-1,-2) and the parabola opens up.
46. The vertex is (-3,-4) and the parabola opens down.
47. Maximum = -6 at x = 10
48. Minimum = 18 at x = -6
In Exercises 49–52, write an equation in standard form of the
parabola that has the same shape as the graph of f(x)
2x?
but with the given point as the vertex.
49. (5,3)
50. (7,4)
51. (-10,-5)
52. (-8,-6)
In Exercises 53-56, write an equation in standard form of the
parabola that has the same shape as the graph of f(x)
or g(x) = -3×2, but with the given maximum or minimum.
53. Maximum = 4 at x = -2 54. Maximum = -7 at x = 5
55. Minimum = 0 at x = 11 56. Minimum = 0 at x = 9
c. From what height was the shot released?
3х2
f(x) = -0.8×2 + 2.4x + 6,
67. Y
where x is the ball’s horizontal distance, in feet, from where it
was thrown.
a. What is the maximum height of the ball and how far from
where it was thrown does this occur?
b. How far does the ball travel horizontally before hitting
Application Exercises
An athlete whose event is the shot put releases the shot with the
same initial velocity but at different angles. The figure shows
the parabolic paths for shots released at angles of 35° and 65º.
Exercises 57–58 are based on the functions that model the
parabolic paths.
F
e
68. Y
F
ei
69. A
ti
S
th
the ground? Round to the nearest tenth of a foot.
c. Graph the function that models the ball’s parabolic path,
60. A ball is thrown upward and outward from a height of 6 feet.
The height of the ball, f(x), in feet, can be modeled by
f(x) = -0.8×2 + 3.2x + 6,
where x is the ball’s horizontal distance, in feet, from where it
was thrown.
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50
is
70. A
tv
F
th
is
71. A
20
D
40
Maximum height
8(x) = -0.04×2 + 2.1x + 6.1
Shot released at 65°
30
Shot Put’s Height (feet)
a. What is the maximum height of the ball and how far from
where it was thrown does this occur?
b. How far does the ball travel horizontally before hitting
the ground? Round to the nearest tenth of a foot.
c. Graph the function that models the ball’s parabolic path.
61. Among all pairs of numbers whose sum is 16, find a pair whose
product is as large as possible. What is the maximum product?
62. Among all pairs of numbers whose sum is 20, find a pair whose
product is as large as possible. What is the maximum product
Maximum height
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fild
Distance of throw or maximum
horizontal distance
10
f(x) = -0.01×2 +0.7x + 6.1.
Shot released at 35°
product?
10
80
90
20 30 40
50
60 70
Shot Put’s Horizontal Distance (feet)
product?
63. Among all pairs of numbers whose difference is 16, find a pair
whose product is as small as possible. What is the minimum
64. Among all pairs of numbers whose difference is 24, find a pair
whose product is as small as possible. What is the minimum
65. You have 600 feet of fencing to enclose a rectangular plot that
borders on a river. If you do not fence the side along the river
find the length and width of the plot that will maximize the
area. What is the largest area that can be enclosed?
72. A
57. When the shot whose path is shown by the blue graph is
released at an angle of 35°, its height, f(x), in feet, can be
modeled by
f(x) = -0.01.x² + 0.7x + 6.1,
where x is the shot’s horizontal distance, in feet, from its point
of release. Use this model to solve parts (a) through (c) and
verify your answers using the blue graph.
a. What is the maximum height of the shot and how far from
its point of release does this occur?
b. What is the shot’s maximum horizontal distance, to the
nearest tenth of a foot, or the distance of the throw?
c. From what height was the shot released?
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cr
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to
73. H
River
$5
ar
a.
*
600 – 2x