Functions
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ALGEBRA: 5.01/ FUNCTIONS 8.F.1,.2,.3 DEFINE EVALUATE AND COMPARE FUNCTIONS - TRANSLATE VARIOUS REPRESENTATIONS OF FUNCTIONS AND IDENTIFY RELATIONS AS LINEAR OR NONLINEAR Functions
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Functions. Algebra: 5.01/ functions 8.f.1,.2,.3 Define evaluate and compare functions - Translate various representations of functions and identify relations as linear or nonlinear. Vocabulary. - PowerPoint PPT Presentation
Transcript of Functions
ALGEBRA: 5 .01 / FUNCTIONS 8 .F.1 , .2 , .3
DEFINE EVALUATE AND COMPARE FUNCTIONS
-T R A N S L AT E VA R I O U S R E P R E S E N TAT I O N S O F F U N C T I O N S A N D I D E N T I F Y R E L AT I O N S A S
L I N E A R O R N O N L I N E A R
Functions
Vocabulary
Function- A rule that relates two quantities so that each input value corresponds to exactly one output value
Input-The value substituted into an expression or function
Output- The value that results from the substitution of a given input into an expression or function
Vocabulary
Domain- The set of all possible input values
Range- The set of all possible output values
Function Notation- The notation used to describe a function. Ex. y=3x2 f(x)= 3x2
f(x) is read “f of x”
Representation
Tables
Graphs
Equations
Representations
Make a table of inputs and outputs Use the table to make a graphx x2+1 y-2-1012
(-2)2+1(-1)2+1(0)2+1(1)2+1(2)2+1
52125
Identify a Function
To determine if a relationship is a function, verify that each input has exactly ONE output
x y0123
5432
One x value has one y value.
This IS a Function!
Identify a Function
The input x=0 has two outputs, y = 3 and y = -3.
Other x values also have more than one y value.
The relationship is NOT a function!
Identify a Function
Make an input-output table and use it to graph y=x2
x y-2-1012
(-2)2=4(-1)2=1(0)2=0(1)2=1(2)2=4
Each input, x, has only one output, y.
The relationship IS a function.
Function Notation
The output value of the function, f that corresponds to the input value x is
written, f(x)
The expression f(x) means “the rule of f applied to the value of x.
Not f multiplied by x
Function Notation
y= x2 = f(x)=x2
The output y is the rule of f applied to x
F(1) = 12 = 1F(1) means evaluate f(x) for x = 1
Evaluating Functions
For each function, find f(0), f(2), and f(-1)
Y= 2x - 1
f(x)=
2x - 1
f(0)= 2(0) – 1
=-1
f(2) =
2(2) – 1 =
3f (-1)=
2(-1) – 1 =
-3
Evaluating Functions
Read the graph to find y for each x
f(0)=
f(2) =
f (-1)=
f(x)= y
-4
-2
-5
Evaluating Functions
Read the table to find y for each x
x y-10123
- 1 25811
f(x)= yf(0)= f(2) =
f (-1)=
28
-1
