Student Activities
Algebra 1
Functions & Function Notations
LESSON 1 Situation 1 Wildebeest
Objectives: (a) Students will be able to graph and analyze data from a given
situation; b) to read and use function notations; and (c) to identify functions and
non-functions.
Materials: Graph
paper, graphing calculators,notebook paper
Instructions:
1) Construct a grid then plot the ordered pairs of data given in the table below.
| Length of droughts(months) | Number of wildebeests | NOTES: |
| 0 1 2 3 4 5 6 7 8 9 10 |
500 400 300 250 200 175 150 125 100 90 75 |
In this situation there are two variables. Variables represent quantities
that change or vary. Questions: (Answer each question first then Click on the number of each problem to check your answer to each question.) |
1. What is meant by
independent and dependent variable?
2. What are the variables in this
situation?
3. Which is the independent variable and
dependent variable in this situation?
4. Does the length of the drought
depends on the number of wildebeest remaining?
5. Is this a function? why? or why not?
6. Can the number of wildebeest be negative or
fractional number? Or can the number of months be negative or fractional number
7. Should the points on the graph be
connected? why or why not?
8. Which variable will be used as the
domain and which will be used as the range? What is the domain and what is the range in
this situation
9. Who would be interested in this data.
FUNCTION NOTATIONS
We can use function notations to ask and to answers questions about the data in a table or
a graph.
EXAMPLE: To ask how many wildebeest is left after 8 months of drought we write: W(8) =
______ reads w of 8 is equal to what? Since 8 coordinates with 100 then the answer is 100
wildebeest would remain after 8 months of drought.
TRY THESE (using function notations)
1. W(__) = 250
2. W(3) = ____
3. W(__) = 125
4. W(12) = ___
5. W(__) = 60
Answers
1. The change in the independent
variable does not depend on the other variable but the change in dependent variable
depends on the change in the independent variable.
2.In this situation one variable
represents length of the drought in months and the other variable represents the
number of wildebeest remaining
3.The length of the drought is the independent
variable and number of wildebeest is the dependent variable since the number of wildebeest
depends on the length of the drought.
4. No, the number of wildebeest depends
on the length of the drought; so the number of wildebeest is the dependent variable and
the length of the drought is the independent variable.
5. This is a function. Since the number of wildebeest
is dependent on the length of the drought we could say it is a function of the the length
of the drought.
6.The number of wildebeest cannot go below zero;
if so they would be extinct. the number of months can be a fraction number but cannot be a
negative number.
7. This function is not continuous and we
should not connect the points.
8. For this data the number of months
is the independent variable and will be called the DOMAIN. The DOMAIN for
this problem will be all non-negative numbers. The number of wildebeest is the dependent
variable; this will be called the RANGE. The RANGE is all whole number
less than or equal to 500.
9. People who work with wildlife and
natural resources would be interested in this information. Knowing about the length of a
drought will help in preventing the extinction of some animals. Problems involving data
and functions can be used in other places other than in algebra classes.
LESSON 2. Situation 2
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