Name ______________________________
1. The functions f(x) and g(x) are defined below.
Solving by Graphing
4. The functions f(x) and g(x) are defined below.
f(x) = 5(x - 5)
g(x) = -2x + 33
Using a table of values, determine the solution to
the equation f(x) = g(x).
Determine where f(x) = g(x) by graphing.
x=4
A.
A. x = 1
B. x = 0
B.
C. x = 33
D. x = 5
C.
D.
x=8
x = -8
x = -6
2. The functions f(x) and g(x) are defined below.
5. The functions f(x) and g(x) are defined below.
f(x) = 15x - 1
g(x) = 14x + 2
Using a table of values, determine the solution to
the equation f(x) = g(x).
A. x = 3
B. x = 44
C. x = -3
B.
D. x = -44
C.
3. The functions f(x) and g(x) are defined below.
f(x) = 3(x + 1) - 5
g(x) = -3x - 7
Using a table of values, determine the solution to
the equation f(x) = g(x).
A. x = -1
B. x = 5
C. x = -7
D. x = 4
Determine where f(x) = g(x) by graphing.
x = -3; x = -2
A.
D.
x = -2
x = -3
x = -4; x = 2
Name ______________________________
6. The functions f(x) and g(x) are defined below.
Determine where f(x) = g(x) by graphing.
x≈0 ; x≈6
A.
B.
C.
D.
B.
x≈0 ; x≈7
C.
x ≈ -3 ; x ≈ 7
D.
By graphing, determine where f(x) = g(x).
x=4
A.
C.
D.
Determine where f(x) = g(x) by graphing.
x = -1; x = 1
A.
x ≈ -3 ; x ≈ 4
7. The functions f(x) and g(x) are defined below.
B.
Solving by Graphing
9. The functions f(x) and g(x) are defined below.
x = -2
x = -3
C.
D.
A.
B.
x=4
x=2
x = -6
x = -1
Approximate the solution to the equation f(x) = g(x)
using three iterations of successive approximation.
Use the graph below as a starting point.
8. The functions f(x) and g(x) are defined below.
B.
x=1
10. Consider the following equations.
x = -7
By graphing, determine where f(x) = g(x).
x=1
A.
x = 1; x = 3
C.
D.
Name ______________________________
Solving by Graphing
x
f(x)
g(x)
2
29
30
Answers
1. D
2. A
3. A
4. A
5. A
6. C
7. A
8. D
9. C
10. B
3
44
44
4
59
58
5
74
72
6
89
86
7
104
100
8
119
114
9
134
128
10
149
142
11
164
156
12
179
170
Explanations
The two functions intersect at the point (3, 44).
1. The solution to the equation f(x) = g(x) is the xcoordinate of the point where the graphs of the
functions intersect.
Create a table of values to find the point of
intersection.
x
0
f(x)
0.0003
g(x)
32
1
0.0016
31
2
0.008
3
Therefore, the solution to the equation is x = 3.
3. The solution to the equation f(x) = g(x) is the xcoordinate of the point where the graphs of the
functions intersect.
Create a table of values to find the point of
intersection.
29
x
-5
f(x)
-4.987654
g(x)
8
0.04
25
-4
-4.962963
5
4
0.2
17
-3
-4.888889
2
5
1
1
-2
-4.666667
-1
6
5
-31
-1
-4
-4
0
-2
-7
1
4
-10
2
22
-13
3
76
-16
4
238
-19
5
724
-22
*Note: Values in the table are rounded where necessary.
The two functions intersect at the point (5, 1).
Therefore, the solution to the equation is x = 5.
2. The solution to the equation f(x) = g(x) is the xcoordinate of the point where the graphs of the
functions intersect.
Create a table of values to find the point of
intersection.
*Note: Values in the table are rounded where
necessary.
Name ______________________________
The two functions intersect at the point (-1, -4).
Solving by Graphing
8. To graphically determine where f(x) = g(x), graph
the two linear functions, and then find the point of
intersection.
Therefore, the solution to the equation is x = -1.
4. To graphically determine where f(x) = g(x), graph
both functions, and determine their point(s) of
intersection.
The two lines intersect at the point (-6, 4).
Therefore, f(x) = g(x) at x = -6.
The two graphs intersect at the point (4, -8).
9. To graphically determine where f(x) = g(x), graph
both functions, and determine their point(s) of
intersection.
Therefore, f(x) = g(x) at x = 4.
5. To graphically determine where f(x) = g(x), graph
both functions, and determine their point(s) of
intersection.
The two graphs intersect at the point (1, 3).
Therefore, f(x) = g(x) at x = 1.
10. First, rewrite the equation so that it is equal to 0.
The two graphs intersect at the points (-3, 2) and (2, -4).
Therefore, f(x) = g(x) at x = -3 ; x = -2.
6. To graphically determine where f(x) = g(x), graph
both functions, and determine their point(s) of
intersection.
The two graphs intersect at the points (0.01..., 2.99...) and (6.94..., 3.94...).
The graph given in the question shows that the
solution to this equation exists between -2 and -1.
Since the solution represents a zero, when the
equation is evaluated at the given bounds, one will
be negative and the other will be positive.
Now, take the average of the upper and lower
bound.
Therefore, f(x) = g(x) at x ≈ 0 and x ≈ 7.
7. To graphically determine where f(x) = g(x), graph
the two linear functions, and then find the point of
intersection.
Evaluate the equation at this value, and determine if
the result is positive or negative.
The two lines intersect at the point (4, -3).
Therefore, f(x) = g(x) at x = 4.
Since the result is positive, treat this as the new
upper bound, and find a new average.
Name ______________________________
Evaluate the equation at this value, and determine if
the result is positive or negative.
Since the result is negative, treat this as the new
lower bound, and find a new average.
Evaluate the equation at this value, and determine if
the result is positive or negative.
Since the result is positive, treat this as the new
upper bound, and find a new average.
Three iterations have been performed giving an
approximate solution of
.
Solving by Graphing