1.2 introduction to relations and functions...1.2 intro to relations and funcs comp.notebook 2...
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1.2 Intro to relations and Funcs comp.notebook
1
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