Foundations Functions Domain and Range Relations Functions Relation
- Slides: 22
Foundations Functions, Domain, and Range
Relations & Functions Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.
Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} State the domain: D: {0, 1, 2, 3} State the range: R: {-6, 0, 4}
Relations and Functions • Relations can be written in several ways: ordered pairs, table, graph, or mapping. • We have already seen relations represented as ordered pairs.
Ordered pair Table {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} Mapping 3 4 7 2 0 -1 -2 0 -5 3 Graph
Functions • A function is a relation in which the members of the domain (x-values) DO NOT repeat. • So, for every x-value there is only one y-value that corresponds to it. • y-values can be repeated.
Functions • Discrete functions consist of points that are not connected. • Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.
Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.
Write the domain and range in {set notation}
Graphs of a Function Vertical Line Test: If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.
Does the graph represent a function? Name the domain and range. x Yes D: all real numbers R: all real numbers y x y Yes D: all real numbers R: y ≥ -6
Does the graph represent a function? Name the domain and range. x No D: x ≥ 1/2 R: all reals y x y No D: all reals R: all reals
Does the graph represent a function? Name the domain and range. x Yes D: all reals R: y ≥ -6 y x y No D: x = 2 R: all reals
Function Notation • When we know that a relation is a function, the “y” in the equation can be replaced with f(x). • f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’. • The ‘f’ names the function, the ‘x’ tells the variable that is being used.
Introducing…… Interval Notation!
List the domain and range in interval notation x Yes D: R: y x y Yes D: R:
List the domain and range in interval notation x No D: R: y x y No D: R:
List the domain and range in interval notation x Yes D: R: y x y No D: R:
List the domain and range in interval notation
Order of Operations (What we use when evaluating the expressions) • • • P E M D A S *Multiply/Divide and Add/Subtract from left to right! Please excuse my dear Aunt Sally?
Examples
Examples • Evaluate the expression.
- Codomain vs domain
- Relation and domain
- Domain and range of relation
- What is the domain and range
- How to know the domain and range of a graph
- Trigonometric functions domain and range
- Trigonometric functions domain and range
- Composite functions domain and range practice
- Domain and range review
- Warm up domain range and functions
- Warm up domain range and functions
- Trig function
- Employee relations in public relations
- Function vs relation
- Range of inverse sine function
- Domain and range of an inverse function
- Domain and range of a rational function
- Constant parent function equation
- Parent function notes
- Domain and range ordered pairs
- Horizontal line test
- Domain of tangent function
- How to graph without a calculator