2.1 Relations and
Functions
In this chapter, you will learn:
 What a function is.
 Review domain and range.
 Linear equations.
 Slope.
 Slope intercept form y = mx+b.
 Point-slope form y – y1 = m(x – x1).
 Linear regression.
What is a function?
FUNCTION
NOT A FUNCTION
FUNCTION
FUNCTION
A function is a special type of
relation in which each type of
domain (x values) is paired of
with exactly one range
value (y value).
NOT A FUNCTION
NOT A FUNCTION
FUNCTION
Relations and Functions
Suppose we have the relation { (-3,1) , (0,2) , (2,4) }
DOMAIN
x - values
-3
1
0
2
2
4
FUNCTION
ONE – TO – ONE
RANGE
y - values
Relations and Functions
Suppose we have the relation { (-1,5) , (1,3) , (4,5) }
-1
5
1
3
4
5
FUNCTION
NOT ONE – TO – ONE
Relations and Functions
Suppose we have the relation { (5,6) , (-3,0) , (1,1) , (-3,6) }
5
0
-3
1
1
6
NOT A FUNCTION
Domain and Range
The set of all inputs, or x-values of a function.
It is all the x – values that are allowed to be used.
The set of all outputs, or y-values of a function.
It is all the y – values that are represented.
Example 1
All x – values or (-∞ , ∞)
 Domain = ________________
 Range = _________________
Just 4 or {4}
Example 2
Just -5 or {-5}
 Domain = ________________
All y – values or (-∞ , ∞)
 Range = _________________
Example 3
All x – values or (-∞ , ∞)
 Domain = ________________
From -6 on up or [-6 , ∞)
 Range = _________________
Example 4
From -6 on up or [-6 , ∞)
 Domain = ________________
All y – values or (-∞ , ∞)
 Range = _________________
Example 5
All x – values or (-∞ , ∞)
 Domain = ________________
All y – values or (-∞ , ∞)
 Range = _________________
Function Notation
What is function notation?
 Function notation, f(x) , is called “f of x” or “a
function of x”.
 It is not f times x .
 Example: if y = x+2 then we say f(x) = x+2.
 If y = 5 when x = 3, then we say f(3) = 5
Example 1
f(x) = 3x + 1
3 (5) + 1 = 16
f( 5) = ____________________
3 (13) + 1 = 40
f( 13) = ____________________
3 (-11) + 1 = -32
f( -11) = ____________________
Example 2
f(x) = x² + 3x - 5
5² + 3 (5) – 5 = 35
f( 5) = ____________________
0² + 3 (0) – 5 = -5
f( 0) = ____________________
4² + 3 (4) – 5 = 23
f( 4) = ____________________