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1 Function and Function Notation

1. The document discusses functions and function notation. It provides examples of relations and uses the vertical line test to determine if they represent functions. 2. Examples are given of evaluating functions for given inputs using function notation. Specific functions are defined equal to expressions involving variables and their evaluations are shown for given values of the variables. 3. One example shows evaluating the expression 2[f(3) – f(1)] given the function f(x) = 2x + 1.

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Ela King
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57 views3 pages

1 Function and Function Notation

1. The document discusses functions and function notation. It provides examples of relations and uses the vertical line test to determine if they represent functions. 2. Examples are given of evaluating functions for given inputs using function notation. Specific functions are defined equal to expressions involving variables and their evaluations are shown for given values of the variables. 3. One example shows evaluating the expression 2[f(3) – f(1)] given the function f(x) = 2x + 1.

Uploaded by

Ela King
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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9/20/2016

Determine whether each relation


is a function.
1. {(2, 3), (3, 0), (5, 2), (4, 3)}
Function and
2 3
f(x)
Function Notation 3
f(x)
0
September 20, 2016
5 2
f(x)

4 3
f(x)

YES, every domain is different!

Functions Determine whether the relation is


A function is a relation in which each element
a function.
of the domain is paired with exactly one 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
element of the range. Another way of
4 1
saying it is that there is one and only one f(x)
output (y) with each input (x). 5 2
f(x) NO,
5
f(x)
3 5 is paired with 2
numbers!
x f(x) y 6
f(x)
6

1 9
f(x)

Function Notation
Is this relation a function?
{(1,3), (2,3), (3,3)}
Input
Output Name of
Function

1
9/20/2016

Vertical Line Test (pencil test) Given f(x) = 3x - 2, find:


If any vertical line passes through more 1) f(3) = 7
than one point of the graph, then that
relation is not a function.
Are these functions?
3 3(3)-2 7
2) f(-2) = -8

-2 3(-2)-2 -8
FUNCTION! FUNCTION! NOPE!

Vertical Line Test Given h(z) = z2 - 4z + 9, find h(-3)

FUNCTION! NO!
-3 (-3)2-4(-3)+9 30
9 + 12 + 9

NO WAY!
h(-3) = 30
FUNCTION!

Is this a graph of a function?

Given g(x) = x2 – 2,
find g(4)

2
9/20/2016

Given f(x) = 2x + 1,
find 2[f(3) – f(1)]

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