Algebra I Lessons 4-1 to 4-4
REVIEW
What are the variables in each graph? Describe how the variables are related at various points on the graph.
1.
The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire
trip. What are the variables? Describe how the variables are related at various points on the graph.
height
Elevation of Hiker
time
a. The variables are height and time. For the c. The variables are height and time. For the
first part of the graph, the height is
first part of the graph, the height is
increasing slowly, which means the hiker
increasing slowly, which means the hiker
is climbing a steep incline. Flat parts of
is climbing a steep incline. Flat parts of
the graph show where the elevation does
the graph show where the elevation does
not change, which means the hiker
not change, which means the trail is flat
stopped to rest. The steep part at the end
here. The steep part at the end of the
of the graph shows that the hiker is
graph shows that the hiker is descending
descending a gentle slope.
a steep incline.
b. The variables are height and time. For the d. All of the above.
first part of the graph, the height is
increasing slowly, which means the hiker
is walking up a gentle slope. Flat parts of
the graph show where the elevation does
not change, which means the trail is flat
here. The steep part at the end of the
graph shows that the hiker is descending
a steep incline.
2.
The graph shows the number of handbags that Mandy made in one day. What are the variables?
Describe how the variables are related at various points on the graph.
number of handbags
Mandy's Handbags
time
In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they
form?
5
6
6
5
1 triangle
3.
6
5
6
6
5
2 triangles
6
5
5
3 triangles
Which of the following represents the above relationship?
a. The perimeter, P, is equal to the length of c. The perimeter, P, is equal to the length of
a side of one triangle multiplied by the
a side of one triangle multiplied by the
number of triangles in the figure, n, plus
number of triangles in the figure, n, plus
two times the length of the base. The
the length of the base. The equation for
equation for the perimeter is
.
the perimeter is
.
b. The perimeter, P, is equal to the length of d. The perimeter, P, is equal to the length of
the base of one triangle multiplied by the
the base of one triangle multiplied by the
number of triangles in the figure, n, plus
number of triangles in the figure, n, plus
the length of another side. The equation
two times the length of another side. The
for the perimeter is
.
equation for the perimeter is
.
4.
triangles?
Suppose you know the perimeter of triangles. What would you do to find the perimeter of
a. Add 5 to the perimeter of triangles
c. Add 12 to the perimeter of triangles
b. Add 6 to the perimeter of triangles
d. Add 10 to the perimeter of triangles
5.
Represent the above relationship by filling in the table below.
Number of
Triangles
Perimeter
1
2
3
6.
Represent the above relationship by drawing a graph.
60
55
50
45
Perimeter
40
35
30
25
20
15
10
5
1
2
3
4
5
Number of Triangles
6
7
The table shows the relationship between the number of sports teams a person belongs to and the amount of free
time the person has per week.
Number of Sports
Teams
Free Time
(hours)
0
46
1
39
2
32
3
25
7.
a. yes
Is the above relationship a linear function?
b. no
8.
What is the graph for the above relationship?
a.
c.
50
45
45
40
40
35
35
Free Time (hr)
Free Time (hr)
50
30
25
20
30
25
20
15
15
10
10
5
5
1
2
3
4
5
1
Number of Sports Teams
b.
d.
45
45
40
40
35
35
30
25
20
20
15
10
5
5
3
4
9.
5
25
10
2
4
30
15
1
3
50
Free Time (hr)
Free Time (hr)
50
Number of Sports Teams
2
Number of Sports Teams
5
1
2
3
4
5
Number of Sports Teams
Describe the above relationship using words. What is the equation for this relationship?
10.
x
y
1
12.3
2
19.6
3
26.9
4
34.2
5
41.5
Graph the function shown by the table. Is the function linear or nonlinear?
a. linear
b. nonlinear
The table shows the total number of squares in each figure below. What is a pattern you can use to complete the
table?
11.
Which of the following equations represents the pattern above?
a.
c.
b.
d.
12.
a.
Which of the following graphs matches the pattern described above?
y
c.
150
135
90
120
80
105
70
90
60
75
50
60
40
45
30
30
20
15
10
1
b.
y
100
2
3
4
5
x
y
d.
200
135
120
140
105
120
90
100
75
80
60
60
45
40
30
20
15
3
4
5
x
3
4
5
x
1
2
3
4
5
x
y
160
2
2
150
180
1
1
13.
The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) represent a function. What is a rule
that represents this function?
a.
c.
b.
d.
14.
The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table
linear? Explain your answer.
Hours Worked
Amount Charged ($)
1
25
2
40
3
60
4
80
15.
A taxi company charges passengers $1.00 for a ride, and an additional $0.30 for each mile traveled. The
function rule
describes the relationship between the number of miles m and the total cost of the ride
c. If the taxi company will only go a maximum of 40 miles, what is a reasonable graph of the function rule?
Write a function for the situation. Is the graph continuous or discrete?
16.
A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs?
What is the graph of each function rule?
17.
18.
19.
Model the function rule
x
with a table of values and a graph.
y
–1
0
1
y
6
4
2
–6
–4
–2
2
–2
–4
–6
4
6
x
Algebra I Lessons 4-1 to 4-4
REVIEW
Answer Section
1.
B
2.
The variables are the number of handbags and time. The flat parts of the graph show either
where Mandy is working on a handbag or taking a break. As soon as Mandy finishes a bag, the graph jumps up a
level to show that she has completed one more bag.
3.
D
4.
A
5.
Number of
Triangles
Perimeter
1
17
2
22
3
27
60
55
50
45
Perimeter
40
35
30
25
20
15
10
5
1
2
3
4
5
6
7
Number of Triangles
6.
7.
A
8.
B
9.
For every sports team the person joins, he or she spends 7 hours per week practicing. So, the
amount of free time the person has, F, is the amount of free time they would have if they did not belong to any
sports teams minus 7 times the number of teams they belong to. In equation form this is
10.
A
11.
D
12.
C
13.
C
.
14.
No, the relationship is not linear. 40– 25 = 15 and 2 – 1 = 1, but 60 – 40 = 20 and 3 – 2 = 1, so the
rates of change vary from $15/h to $20/h.
20
C
18
16
14
12
10
8
6
4
2
10
20
30
40
m
15.
16.
C = 11n; discrete
y
4
2
–4
–2
2
–2
–4
17.
4
x
y
4
2
–4
–2
2
4
x
–2
–4
18.
19.
x
y
–1
17
0
6
1
–5
y
24
16
8
–24
–16
–8
8
–8
–16
–24
16
24
x