Relations & functions With Domain & Range

Relations A set of ordered pairs or a data table.

A set of ordered pairs or a data table.

Function A set of ordered pairs or a data table in which the x’s don’t repeat.

A set of ordered pairs or a data table in which the x’s don’t repeat.

Function? (-2, 4), (-1, 1), (0,0), (1,1), (2,4) Yes (-2, 4), (-1, 1), (0,0), (-1,1), (-2,4) No

(-2, 4), (-1, 1), (0,0), (1,1), (2,4)

Yes

(-2, 4), (-1, 1), (0,0), (-1,1), (-2,4)

No

Function rule An equation that describes a function

An equation that describes a function

Example: y=3x+4 3x+4=y 4+3x=y Same equation

y=3x+4

3x+4=y

4+3x=y

Same equation

y =3 x +4 OUTput (dependent variable) INput (independent variable)

Function Machine

Function Machine

Terms to use x Independent Variable Input Domain y Dependent Variable Output Range

x

Independent Variable

Input

Domain

y

Dependent Variable

Output

Range

Domain & Range Just a list of the x’s or y’s in brackets { }. Usually from least to greatest

Just a list of the x’s or y’s in brackets { }.

Usually from least to greatest

Domain & Range D={x, x, x} {list the x’s. Leave out duplicates.} R={y, y, y} {list the y’s. Leave out duplicates.}

D={x, x, x}

{list the x’s. Leave out duplicates.}

R={y, y, y}

{list the y’s. Leave out duplicates.}

Find Domain & Range (-2, 4), (-1, 1), (0,0), (1,1), (2,4) For the domain, grab the x’s D={-2, -1, 0, 1, 2} For the range, grab the y’s R={0, 1, 4}

(-2, 4), (-1, 1), (0,0), (1,1), (2,4)

For the domain, grab the x’s

D={-2, -1, 0, 1, 2}

For the range, grab the y’s

R={0, 1, 4}

Evaluate the function rule: y= x – 1 for x = -2 y= ( ) – 1 Don’t forget those ( )! y= ( -2 ) – 1 y= -3

y= x – 1 for x = -2

y= ( ) – 1

Don’t forget those ( )!

y= ( -2 ) – 1

y= -3

Find the range for the function: When the domain is {-3, 0, 3} p = 4q – 6 y = 4x – 6 (this is the one you put in your calculator!)

When the domain is {-3, 0, 3}

p = 4q – 6

y = 4x – 6 (this is the one you put in your calculator!)

Find the range for the function: Write it three times: y = 4( -3 ) – 6 y= y = 4( 0 ) – 6 y= y = 4( 3 ) – 6 y=

Write it three times:

y = 4( -3 ) – 6 y=

y = 4( 0 ) – 6 y=

y = 4( 3 ) – 6 y=

Find the range for the function: Make sure your stat plot is off. Go to y= and enter the equation y = 4x – 6 Enter 2 nd /Graph to get the TABLE See your answers?

Make sure your stat plot is off.

Go to y= and enter the equation y = 4x – 6

Enter 2 nd /Graph to get the TABLE

See your answers?

Find the range for the function: Write it three times: y = 4( -3 ) – 6 y= -18 y = 4( 0 ) – 6 y= -6 y = 4( 3 ) – 6 y= 6

Write it three times:

y = 4( -3 ) – 6 y= -18

y = 4( 0 ) – 6 y= -6

y = 4( 3 ) – 6 y= 6

Review Function? Relation? Domain? Range? Function rule?

Function?

Relation?

Domain?

Range?

Function rule?