Algebra II, Unit 1
Activity
Matching the Pattern
Refer to your Function Toolbox to help match each data set, equation, table, or
description to the function that it seems to match best. Students should work in
groups to complete this activity. Be prepared to justify your selections.
1.
Price
Charged
Daily
Customers
$20
$30
$40
$50
$60
100
70
40
20
10
2.
When businesses do market research for new products, they are
interested in the relation between the prices they charge and the
income they will receive from sales. For example, suppose that
the owners of Video City are trying to set the best rental price
for video game cartridges. Their market research staff might
produce a recommendation that says: Profit (in dollars per
week) depends on charge per rental (in dollars) according to
the rule
P = –750 + 900C – 150C2
HCPSS Common Core Algebra II
Algebra II, Unit 1
Activity
3.
4.
In public transportation systems of most U. S. cities, the fare is
generally related to distance traveled and time of day (higher in
morning and evening rush hours). The fare pattern for one city’s
subway system is illustrated in the following table.
Distance (in
miles)
Fare (in $)
1
1.10
2
3
4
5
6
7
1.20
1.30
1.40
1.50
1.60
1.70
8
1.80
5.
In the NASA explorations of space, six missions took
astronauts to landings on the Moon. One other mission
landed a spacecraft, but not astronauts, on Mars. The time
required to reach a destination depends on the distance
and the speed of the spacecraft. For example, the Moon is
about 400,000 kilometers from the Earth. You can calculate
time T for that trip from average speed S by the rule
T=
400, 000
S
.
HCPSS Common Core Algebra II
Algebra II, Unit 1
Activity
6.
Number of Tickets
Sold
0
50
100
150
200
250
300
Dollars of
Income
0
125
250
375
500
625
750
7.
A soccer kick had height a function of time in flight that could
be modeled well by the rule
h(t) = -16t2 + 50t.
8.
As the number of employees increases, the cost per
employee decreases.
HCPSS Common Core Algebra II
Algebra II, Unit 1
9.
10.
Suppose that for a spring used in weight training
equipment its length L (in feet) is related to the force
pulling on it F (in pounds) by the rule L = 2 + 0.01F.
11.
The stopping distance D of a car depends on reaction distance
R and braking distance B. Each of these variables is a function
of the speed s of the car. You can calculate reaction distance
and braking distance in feet by using the rules:
R = 1.1s and B = 0.05s 2
where s is the speed of the car in miles per hour.
HCPSS Common Core Algebra II
Activity
Algebra II, Unit 1
Activity
12.
13.
The bowhead whale population is represented by the equation
y = 5700(1.03)x , where x represents the number of years after 1992.
14.
x
y
1
1
HCPSS Common Core Algebra II
2
2
3
4
4
8
5
16
6
32
7
64
8
128
Algebra II, Unit 1
Activity
Matching Patterns
1.
2.
3.
4.
5.
6.
7.
8.
Power
Quadratic
Quadratic
Linear
Power
Linear
Quadratic
Power
HCPSS Common Core Algebra II
9.
10.
11.
12.
13.
14.
Quadratic
Linear
Quadratic
Linear
Exponential
Exponential