Today’s AgendaAttendance / Announcements

◦Projects due◦No Quiz Friday (exam week)◦Need Graphing Calculators (TI-83,84,..)

Section 3.1

FunctionsA function is a rule (think: operation) that assigns an input value to exactly one specific output

f(x) can be thought of as “y”

Examples…before we really define what a function is.

32 xy 32)( xxf

xxy 323 2 ttth 323)( 2

xy 3 xxg 3)(

A function is a rule (think: operation) that assigns an input value to exactly one specific output

inputs

outputs

f(x)

Domain

Range

Determine if each relation is a function or not…

9 4 1 0 1 4 93 2 1 0 - 1 - 2 - 3

“Functions need to be predictable!”

Determine if each relation is a function or not… -2 -1 0 3 4 6 9

3 2 1 0 1 2 3 Since it is a function, it has a domain and range:

Domain (set of all inputs): { }

Range (set of all outputs): { }

Function Notation (p. 137)

Evaluating Functions,2)( 2 xxxfif

)3(f

)3(f

)(tf

)3(xf

“The Difference Quotient”

The difference quotient for a function f(x) is:

h

xfhxf )()(

Substitute, Subtract, and Simplify

h

xfhxf )()( Find the difference quotient of: 53)( xxf

h

xfhxf )()(

Find the difference quotient of:

53)( xxf

h

xfhxf )()(

Find the difference quotient of:

1)( 2 xxf

Finding Domains of Functions

The domain of a function is the set of values where the function is defined.

So, to find domains, we need to think about where functions are NOT defined!

Finding Domains of Functions

Red Flags

• Zero(s) in the denominator• Negative under square root

Finding Domains of Functions 

 

Finding Domains of Functions

Finding Domains of Functions

h (𝑥 )= √𝑥𝑥2−3 𝑥+2

Classwork / Homework

Page 140 9 – 19 odd,

23 – 29 odd, 35 – 45 odd, 51