Math 1314
College Algebra
Section 2(2)
Functions
Definitions and Examples
A set of ordered pairs
{ (2,3) , (4,7) , (-1,-5) }
Yes
{ (2,3,5) , (4,7) , (-1,-5) }
No
{ (-2,-3) , (-2,7) , (-2,-5) }
Yes
Definitions and Examples
A relation in which each
x has only one y value.
(x can’t repeat)
{ (2,3) , (4,7) , (-1,-5) }
Yes
{ (2,5) , (4,5) , (-1,-5) }
Yes
{ (-2,-3) , (-2,7) , (7,-5) }
No
Functions by Graphing
A vertical line will touch a function only one time
Function
Not a
Function
Function
Functions Algebraically
We use f(x) =, g(x) = , h(x) = …. to define a
function rather than y =
f ( x)  2x2  6x rather than y  2x2  6x
g ( x)  7 x  4 rather than y  7 x  4
3x  5
3x  5
h( x ) 
rather than y 
7x  8
7x  8
This tells us the letter x will be the variable
Telling if something is a function
If you can solve for y = a single value you have a function
2 y  4x  8  0
Solve for y:
y  2 x  4
This is a function with domain: 
y  3x  2  0
2
Solve for y:
y  3x  2
2
This is a function with domain: 
x y 4  0
2
Solve for y:
y   4 x
This IS NOT a function (+ is two parts)
Evaluating an Algebraic function
Find each if: f ( x)  2 x  5 and g ( x)  7  4 x
f (2)  2(2)  5  9
g (0)  7  4(0)  7
f (2)  2(2)  5  1
g (2w)  7  4(2w)  7  8w
f (2a  1)  2(2a  1)  5  4a  3
Definitions and Examples
The set of all x-values
The set of all y-values
Domain
Range
{ (2,3) , (4,7) , (-1,-5) }
{-1,2,4}
{-5,3,7}
{ (2,5) , (4,5) , (-1,-5) }
{-1,2,4}
{-5,5}
{ (-2,-3) , (-2,7) , (7,-5) }
{-2,7}
{-3,-5,7}
Domain & Range Algebraically
Fractions
Domain: All Real Numbers Denom  0
Range: All Real Numbers  Front
x2
f ( x) 
2x  3
Domain :  
3
2
Range :   12
Domain & Range Algebraically
Polynomials
Domain: All Real Numbers = 
Range: Look at the graph – frequently
will be all real numbers = 
f ( x)  3x  4x  5
Domain : 
g ( x)  2x  7 x  1
Domain : 
h( x)  x  3x 1
Domain : 
3
5
2
4
Domain & Range Algebraically
Square Roots
Domain: Inside > 0
Range: All Real Numbers > 0
(unless there are numbers
outside the root)
f ( x)  2x  4
Domain :   2
Range :   0
h( x)  5x  2
Domain :   52
Range :   0
Increasing, Constant, and Decreasing functions
a
b
c
d
Intervals where Increasing
(c, d )
Intervals where Decreasing
(a, b)  (d , e)
Intervals where Constant
(b, c)
e
Opportunity to share
1) 3-Decimal Distance between
 2 , 7  and
2) 3-Decimal Midpoint between
 2 , 7  and

3,  5


3,  5

3) Center and Radius of
x  y  4x  6 y  5  0
2
2