Name: ______________________
Class: __________________
AU2: Notes # 2 – Relations and Functions
Date: __________________
Vocabulary:
Function is a relationship that assigns exactly one output value for each input value.
Relation is a set of ordered pairs.
Domain is the possible values for the input, or independent variable of the function, the x value.
Range is the possible values for the output, or the dependent variable of the function, the y value.
Example 1:
y  x  1 is a function that maps exactly one y-value from each x-value
x
-2
-1
0
1
2
x 1
 2  1
 1  1
0  1
1  1
2  1
y
-1
0
1
2
3
x, y 
 2,  1
 1, 0
0,1
1, 2
2, 3
In the table above identify the domain, range, and relation.
Function Notation is when you use f x  to indicate the outputs. You read f x  as “f of x” or “f
is a function of x”. Other examples are g x or hx  .
In the table above, rewrite the equation so that it is in function notation.
1
Vertical-line test: if a vertical line on a graph passes through more than 1 point, it is not a
function.
Example 2: Using the Vertical-Line Test: Determine whether the relation
{(0,-2), (1,-2), (-3, 1), (-2, 0), (-1,-1), (3, 2), (2,-3)} is a function.
Try It
a)
b)
c) Determine whether the following relation is a function:
{(0,-4), (1,-3), (-3, 2), (1, 0), (-1,2), (3, 2)}.
2
Example 3: Using a Mapping Diagram: Determine whether each relation is a function.
{(4, 3), (2,-1), (-3,-3), (2, 4)}
Try It
Use a mapping diagram to determine whether each relation is a function.
a. {(3, -2), (8, 1), (9, 2), (3, 3), (-4, 0)}
b. {(6.5, 0), (7, -1), (6, 2), (2, 6), (5, -1)}
Example 4: Making a Table From a Function Rule
Make a table for  5x  25  f x and evaluate the function to find the range for the
domain values of {-2, 0, 2, 4}.
x
f x 
3
Example 5: Determining solutions
a) Is the ordered pair (-2, -2) a solution to the function y  3 x  8 ?
2
b) Is the ordered pair (-3, 7) a solution to the function f  x    x  5 ?
3
Example 6: Finding values
a) Given: f(x) = 7x + 4. Find x when f ( x)  53.
b) Given: f ( x)  x 2  4 . Find f (3).
c) Given: f ( x)  5 x  3 . Find x when f ( x)  18.
4