1.2 Introduction to Relations and Functions...1.2 Intro to relations and Funcs comp.notebook 2...
Transcript of 1.2 Introduction to Relations and Functions...1.2 Intro to relations and Funcs comp.notebook 2...
1.2 Intro to relations and Funcs comp.notebook
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August 11, 2021
Aug 107:18 AM
1.2 Introduction to Relations and Functions
Number line
Inequality notation
Set builder notation
Interval notation
TYPES OF INTERVALS
Open x>aa<x<bx<b
Closeda≤x≤b
Otherx≥aa<x≤b
Disjointx<a or x>b
All real numbers
No solution
Ex. 1
Write the following in all notations and describe the type of interval.
a) x>7 b) {x|3≤x≤5} c) (∞,2]
We have different ways to represent solutions sets.
1.2 Intro to relations and Funcs comp.notebook
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August 11, 2021
Aug 107:18 AM
Relations
A relation is a set of ordered pairs.
S={(4,2),(0,5),(3,6)}
Domain is the
Range is the
Graph of a relation
A graph of a line or curve in the xy plane represents a relation.
Ex.2 Let relation R=(x, 3x). Complete the table and graph the relation.
Mapping Diagrams
We can use diagrams to show relations.
Ex.3 Draw a mapping diagram to represent the data in example 2. Give the domain and range.
y
x5
5
5
5
1.2 Intro to relations and Funcs comp.notebook
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August 11, 2021
Aug 107:18 AM
FUNCTIONS
A function is a relation in which each element in the domain corresponds to exactly one element in the range.
Domain 'x' variable, independent var, input
Range 'y' variable, dependent var, output
EX.5Is {(1,2),(2,4),(5,6), (9,4)} a function?
Domain
Range
TRYIs a function?
Find the domain and range.
EX.6Is {(x,y)| y=3x1} a function? Find the domain and range.
x 2 3 3 5y 2 4 7 8
1.2 Intro to relations and Funcs comp.notebook
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August 11, 2021
Aug 107:18 AM
Domain and Range from Graphs
EX.4Give the domain and range of the given the graphs below.
a) b)
Domain and range from a calculator?
1.2 Intro to relations and Funcs comp.notebook
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August 11, 2021
Aug 107:18 AM
Vertical Line Test
If a vertical line intersects a graph in no more than one point, then the graph is a function.
Ex.6Is the graph a function?
a) b)
Function Notation
Instead of writing y, we use f(x) this is read as 'f of x'.
Ex.7For each function find f(4)
a) f(x) = 2x+5 b)
Ex.8For each function find f(1)
a) b)
Ex.9Evaluate the following expressions given f(x)=3x8
a) f(2) b) f(a)
c) f(a+h) d) f(7x)
x 3 4 5 6f(x) 5 2 1 4