types of functions:. linear quadratic absolute value
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Types of functions:
Linear
bmxy
Quadratic
cbxaxy 2
Absolute Value
xy
Exponential xbay )(
Constant
by
Polynomial
Step
Trigonometric
Logarithmic
Square Root Functions
Rational Functions
Vocabulary•Relation – a set of ordered pairs Example – {(-1,1), (2,3), (2,1), (2,-1),
(5,1)}
•Function – a relation for which each x corresponds to exactly one y
Use the vertical line test to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.
Vertical Line Test
This graph is a function since there are no vertical lines that hit the graph more than once.
Ways of showing functions:
• Graphically- use vertical line test!
Ways of showing functions:
• Equations - use your calculator to see the graph
262 2 xxxf
•Tables (functions have no repeated x’s) Ex of function ex of non-function
x y
-3 9
-3 4
-1 1
0 0
1 1
2 4
3 9
x y
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9
• Mappings – look to see if every element of the first set has ONLY ONE element it matches in the second set.
Set notation (set builder and interval notation) • Set builder notation: The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." The set {x: x ≠ 3} is the set of all real numbers except 3
The set {x | -2 < x < 5} is the set of numbers such that values of x are greater than negative 2 and less than 5.
• Interval notation:
A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.
Another example: The interval: which includes -1 and excludes 2.