Download 2.1 Function/Relation Notes

Algebra 2 – Relations and Functions
Name __________________________
I. What is a function?
Definition:
__________________________________________________________________________________
Draw a representation of a “function machine” here:
When y is a function of x, this means ___________________________________________________
2. Function vocabulary:
Domain: _____________________________________________
Range: ______________________________________________
Remember! If a relation is a function there cannot be more than _______ possible output value for
each _______________ value.
3. Using a verbal description to identify a function
a. Consider the relationship of CHS student ID numbers and student locker numbers. Write “ID #”
in the input box and “locker number” in the output box.
Is a student’s locker number a function of their ID number? Why or why not?
Complete the boxes below:
4. Which of the following tables represents a function? Explain your answer.
Input
Out
put
-3 2
5 1
5 8
7 15
Input
Output
-3
5
6
7
2
2
2
2
5.
Evaluating Functions
f ( x) reads _________________
f is _______________________
( x) in the parentheses means ______________________________________
For example...
If g ( x)  2 x  5 then g (3)  11 , where
is ___________________________________
is ___________________________________ and
11
is __________________________________ (why?)
You try it!
If
f ( x)  5  3x
evaluate:
a)
f (3) 
b)
f ( 2) 
c)
f ( A) 
f (3)  4
f ( 2)  11
f ( A)  5  3 A
Example 1: State the domain and range of the relation. Determine if the relation is a function.
 6,1, (5,9), (3,7), (1,7), (6,9)
You Try: State the domain and range of the relation. Determine if the relation is a function.
x
y
2
-2
-1
-1
-2
0
-1
1
2
2
A relation in which the domain is a set of individual points, like the relation in the graph below is said to
be a discrete relation. Notice that its graph consists of points that are not connected.
y=#of runs
X=innings
When the domain of a relation has an infinite number of elements and the relation can be drawn with a
line or smooth curve, the relation is a continuous relation.
When using the graph of a relation (both discrete and continuous, you can use the vertical line test to
determine if a relation represented by the graph is a function.


If a vertical line can be drawn that hits the graph at more than one point = NOT a function.
If a vertical line can be drawn that hits the graph at only one point = Is a function.
EX: Determine if the relation is a function.