Lesson 31
S.W.B.A.T: Identify the independent and dependent variable in sentence. Write a
function rule for a table and a situation.
DO NOW
1.
If 𝑓(𝑥) = 2𝑥 − 1, find f(3).
2. If f(x) = 2x -1, what is x when f(x) = 21?
Example 1
Determine a relationship between the x-and y-values. Write a function rule (equation) that
describes this relationship.
Step 1
List all the possible relationships between the first pair of x- and y-values.
Try one or more of the following operations: + - × ÷ ( )2
√
Possible Relationship #1:
Possible Relationship #2:
-4 _____________ = -1
-4 ________________ = -1
Possible Relationship #3
Possible Relationship #4
-4 ________________ = -1
-4 ________________ = -1
Step 2
See if each operation works for every other xy pair. Choose one that fits every
pair.
Step 3
Write the final answer in function notation: _________________________
Example 2
Write a function rule for the ordered pair.
Exercise 1 Write a function rule that describes each ordered pair.
Express your final answer in function notation.
1)
2)
3)
Writing a Function Rule from a Situation
When writing a function rule from a description of a situation. There are three major steps that
you have to follow:
1) Identify the independent and dependent variables. The dependent variable is the one that
depends on the other. (e.g. A person’s wages depends on the number of hours they work)
The independent variable marches on by itself (such as time), and is the one you must know first
before figuring out the other one.
2) Label the independent variable x and the dependent variable y.
3) Write a function rule using 𝒇(𝒙) notation.
4) State an appropriate domain. Think of what x can be and can’t be. For example, can x be
anything, even fractions? Negatives? If not, state which x-values your rule includes. Use setbuilder notation when possible.
Example 3
A lawyer’s fee is $200 per hour for her services. Write a function rule for this situation.
State an appropriate domain for your function.
Steps 1 and 2- Identify and label the independent and dependent variables.
Dependent Variable (y)
Independent Variable (x)
3) Function Rule: ______________________________________________
4) Appropriate Domain: __________________________________________
Why did you choose this domain?
______________________________________________________________________________
__________________________________________________
Example 4
Sequences are a special type of function that is an ordered list of numbers or pictures (called
terms). For example, the list of odd integers is a type of sequence:
1, 3, 5, 7, 9, …
In a sequence, the number of the term (position) is the independent variable. We can come up
with a rule to find the term given its position in the sequence.
The number of the term (the independent variable) is symbolized by 𝑛.
The term of the sequence (the dependent variable) is symbolized by 𝑓(𝑛).
For example, the odd numbers listed above can be generated by the function rule
𝑓(𝑛) = 2𝑛 − 1
because 𝑓(1) = 2(1) − 1 = 𝟏
𝑓(2) = 2(2) − 1 = 𝟑
𝑓(3) = 2(3) − 1 = 𝟓,
and so on……..
Exercise 2
Identify the independent and dependent variables in each situation. Write a function rule to
describe each situation. State an appropriate domain.
1) A local carnival charges $8 for admission plus $1.50 per ride.
𝑦 = ______________________________________ (dependent variable)
𝑥 = ______________________________________ (independent variable)
Function Rule: _______________________________________________
Appropriate Domain: _______________________________ (use set-builder notation)
2) A contractor charges $75 per hour.
𝑦 = ______________________________________ (dependent variable)
𝑥 = ______________________________________ (independent variable)
Function Rule: _______________________________________________
Appropriate Domain: _______________________________ (use set-builder notation)
3) The length of a rectangle is 3 more than twice the width.
𝑦 = ______________________________________ (dependent variable)
𝑥 = ______________________________________ (independent variable)
Function Rule: _______________________________________________
Appropriate Domain: _______________________________ (use set-builder notation)
4) The numerator of a fraction is three times its denominator.
𝑦 = ______________________________________ (dependent variable)
𝑥 = ______________________________________ (independent variable)
Function Rule: _______________________________________________
Appropriate Domain: _______________________________ (use set-builder notation)
Exercise 3
1) Consider the following sequence.
1
2
3
4
Describe the independent variable. ______________________________________
Describe the dependent variable. ________________________________________
Function Rule: ______________________________________ (remember to use 𝑓(𝑛), 𝑛𝑜𝑡 𝑓(𝑥)!)
Appropriate Domain: _______________________________ (use set-builder notation)
EXIT
2) Determine a function rule 𝑓(𝑛) for the following sequences:
Sequence
a)
𝑛
𝑓(𝑛)
1
3
2
6
3
9
4
12
b) 2, 4, 6, 8, 10……
c) 4, 5, 6, 7, 8…
Function Rule
Lesson 31 Homework
Determine a relationship between the x- and y-values. Write an equation in function notation
𝑓(𝑥) to describe the relationship.
______________________________________
_____________________________
5)
a) Write a function rule to describe the total cost of attending the class. ________________
(use f(x) notation)
b) Describe what domain you would use for this function and why. __________________
__________________________________________________________________________
c) What would be the range of this function? ____________________________________
6) Determine a function rule for the following sequence. Use 𝑛 for the number of the term.
and let 𝑓(𝑛) be the term of the sequence:
1, 6, 11, 16, ….
Function Rule: ________________________________________