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.
a. / The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. Flat parts of the graph show where the elevation does not change, which means the hiker stopped to rest. The steep part at the end of the graph shows that the hiker is descending a gentle slope. / c. / The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. 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.b. / The variables are height and time. For the 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. / d. / All of the above.
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.
In the diagram below, what is the relationship between the number of triangles and the perimeter of the figure they form?
3.Which of the following represents the above relationship?
a. / The perimeter, P, is equal to the length of a side of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of the base. The equation for the perimeter is . / c. / The perimeter, P, is equal to the length of a side of one triangle multiplied by the number of triangles in the figure, n, plus the length of the base. The equation for the perimeter is .b. / The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus the length of another side. The equation for the perimeter is . / d. / The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of another side. The equation for the perimeter is .
4.Suppose you know the perimeter of triangles. What would you do to find the perimeter of triangles?
a. / Add 5 to the perimeter of triangles / c. / Add 12 to the perimeter of trianglesb. / 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 / Perimeter1
2
3
6.Represent the above relationship by drawing a graph.
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.Is the above relationship a linear function?
a. / yes / b. / no8.What is the graph for the above relationship?
a. / / c. /b. / / d. /
9.Describe the above relationship using words. What is the equation for this relationship?
10.
x / y1 / 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. / nonlinearThe 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.Which of the following graphs matches the pattern described above?
a. / / c. /b. / / d. /
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 with a table of values and a graph.
x / y–1
0
1
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 / Perimeter1 / 17
2 / 22
3 / 27
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.
15.
16.C = 11n; discrete
17.
18.
19.
x / y–1 / 17
0 / 6
1 / –5