Functions - Lone Star College System
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Transcript Functions - Lone Star College System
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
x2
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