Algebra
Name _______________________________________
TRANSFORMATIONS UNIT
Period ______ Date ____________________________
Function Notation (Day 2)
1.
The cost in dollars of renting a bicycle in Pismo Beach is a
function of the number of hours the bike is rented. The
relationship between both variables can be modeled as
𝐶(𝑡) = 4.5𝑡 + 10.
a) Find the value of 𝐶(3). Write a sentence to interpret your
answer in the context of the problem.
b) Solve the equation 𝐶(𝑡) = 41.5. Write a sentence to
interpret your answer in the context of the problem.
2.
The weigh measured in pounds of a teenager boy can modeled
as a function of his height measured in inches. The relationship
between both variables is
𝑤(ℎ) = 3.5ℎ − 108.
a) Find the value of 𝑤(72). Write a sentence to interpret your
answer in the context of the problem.
b) Solve the equation 𝑤(𝑡) = 120. Write a sentence to
interpret your answer in the context of the problem.
3.
The number of bacteria growing in a Biology experiment
can modeled as a function of the number of days since the
experiment began. The relationship between both
variables is
𝑏(𝑡) = 250(1.25)𝑡 .
a) Find the value of 𝑏(0). Write a sentence to interpret
your answer in the context of the problem.
b) Find the value of 𝑏(7) (you may use a calculator for this
question.) Write a sentence to interpret your answer in
the context of the problem.
c) What is the daily percent of increase for the bacteria
population?
4.
Patty Patriot wants to host an end-of-the-year party at her house. The number of hours it
takes to get the house clean and decorations ready is a function of the number of people
helping. The relationship between both variables is
60
ℎ(𝑝) = .
𝑝
a) Find the value of ℎ(1). Write a sentence to interpret your answer in the context of the
problem.
b) Find the value of ℎ(15). Write a sentence to interpret your answer in the context of the
problem.
c) Solve the equation ℎ(𝑝) = 5. Write a sentence to interpret your answer in the context of
the problem.
SEE OTHER SIDE
In problems 5-10, given the table shown below, find the value of each expression.
x
−4
−3
−2
−1
0
1
2
𝑟(𝑥)
6
−2
−6
7
5
−1
−2
𝑠(𝑥)
1
−5
0
−6
2
−1
3
5.
𝑟(3) =
6.
𝑠(−4) =
7.
8.
2𝑠(0) − 3𝑟(4) =
9.
7𝑟(−2) ∙ 𝑠(1) =
10.
3
0
1
4
3
−3
5𝑟(−1) =
𝑠(0)
𝑟(2)
=
In problems 11-16, use the table shown above to solve each equation.
11. 𝑟(𝑥) = 0; 𝑥 =?
12. 𝑠(𝑥) = 1; 𝑥 =?
13. 2𝑟(𝑥) = 12; 𝑥 =?
14. 𝑠(𝑥) + 3 = 5; 𝑥 =?
15. 𝑠(𝑥) = 𝑟(𝑥); 𝑥 =?
16. 𝑟(𝑥) = −𝑠(𝑥); 𝑥 =?
In problems 17-19, solve each system using the indicated method:
17.
Solve using substitution:
18.
Solve using elimination:
3𝑟 − 4𝑡 = −10
4𝑤 + 3𝑧 = −3
{
{
6𝑟 − 𝑡 = −6
5𝑤 = 2𝑧 + 25
19.
Solve by graphing. Check your answer.
𝑦 = −𝑥 + 5
{
5𝑦 − 3𝑥 = −15
Solution:
Check: