Function Review

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Nonlinear

not a straight line

Linear

straight line

graph

the DIAGRAM that represents a function or function table on the coordinate plane

input

the first coordinate (value) of an ordered pair in a relation (x,y)

FUNCTION

(-1, 0) (0, 1) (1, 6) (2, 2)

FUNCTION

(-3, 0) (-1, 2) (0, 2) (2, 3)

RELATION

(-5, 3) (-5, 2) (3, 7) (3, 8)

RELATION

(0, 1) (0, -1) (2, 3) (-2, 3)

FUNCTION

(1, 2) (3, 4) (4, 5) (5, 2)

Nonlinear

(1, 2), (2, 5), (3, 6)

Linear

(1, 2), (2, 5), (3, 8)

RELATION

(1, 3) (2, 4) (2, 5) (3, 9)

Consider the function rule: f(x)=2x+5, find the value of f(-10)

-15

Consider the function rule: C(d)=5d-12, find the value of C(-8)

-52

Consider the function rule: f(x)=2x+5, find the value of f(10)

25

Linear

2x + y = 10

Consider the function rule: C(d)=5d-12, find the value of C(10)

38

A special relation where every input (independent variable) value has ONLY ONE output (dependent variable) value

A function

y = $25x + $50

A plumber charges $50 for a service call and $25 per hour in labor costs.

Any relation between 2 variables ( independent and dependent)

A relation

Domain

A set of input or x-values

Range

A set of output or y-values

Vertical Line Test

A test to check whether the given graph is a function

domain

ALL possible x-values in a function

range

ALL possible y-values in a function

y = $0.75x + $7.95

Cost of a pizza plus 75 cents for each additional topping.

y = $10x + $4.75

Cost to join a book club has a one time fee and a monthly charge of ten dollars.

Express the relation as a table and a graph. Then state the domain and range. {(3, 2), (-2, 4), (4, -4), (4, 0), (-1, -3)}

D: {-2, -1, 3, 4}; R: {-4, -3, 0, 2, 4}

Express the relation as a table and a graph. Then state the domain and range. {(-1, -5), (2, -3), (3, -2), (5, 1), (-4, 2)}

D: {-4, -1, 2, 3, 5}; R: {-5, -3, -2, 1, 2}

Function graph- passes the vertical line test

Is this a function?

Function mapping diagram - each input has exactly one output

Is this a function?

Not a function graph- does not pass the vertical line test because when x=0, the y-values are 3 and -3

Is this a function?

Not a function graph- does not pass the vertical line test because when x=0, the y-values are 3 and -5

Is this a function?

Not a function mapping diagram- there is an input (2) that goes to two different outputs (B and C).

Is this a function?

Not a function mapping diagram- there is an input (4) that goes to two different outputs (5 and -5).

Is this a function?

Are all relations functions?

No, because not all relations have special relationship like functions

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-2, -1), (0, 3), (5, 4), (-2, 3)

No, it is not a function Domain: -2, 0, 5 Range: -1, 3, 4

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-1, 7), (0, -3), (1, 10), (0, 7)}

No, it is not a function. Domain: -1, 0, 1 Range: -3, 7, 10

What is the domain and range of the following relation? Is it a function? {(1, -2), (-2. 0), (-1, 2), (1, 3)}

No, it is not a function. Domain: -2, -1, 1 Range: -2, 0, 2, 3

Is this relation a function? If not, explain why. (-2,-2) (2,-1) (3,0) (5,3) (5,4)

No, this relation is not a function because the ordered pair (5,3) and (5,4) have the same input but different outputs.

Is this relation a function? If not, explain why. (-3,-1) (-2,0) (-1,3) (-1,0) (0,-1)

No, this relation is not a function because when x=-1, the y-values are 3 and 0.

graph of the function

The set of all coordinate points (x, y) that forms a graph in the xy-plane.

if any vertical line crosses a graph in more than one point it is not a function (one x-value has more than one y-value)

What is the vertical line test?

If each number in the domain has an arrow to only one number in the range.

When does the mapping diagram represent a function?

Are all functions relations

Yes, because relations mean any form of relationships between 2 variables including special relation such as functions

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-1, 5), (0, 3), (2, 3), (3, -1)}

Yes, it is a function Domain: -1, 0, 2, 3 Range: 5, 3, -1

Draw the mapping diagram for the relation and determine whether it is a function or not. {(2, 4), (- 8, 0), (1, 5), (3, 1)}

Yes, it is a function.

What is the domain and range of the following relation? Is it a function? { (-1,2), (2, 51), (1, 3), (8, 22), (9, 51) }

Yes, it is a function. Domain: -1, 2, 1, 8, 9 Range: 2, 51, 3, 22, 51

output

the second coordinate (value) of an ordered pair in a relation (x, y)

ordered pair

the x- and y-value of a point in (x, y) order

Nonlinear

x = 4

Linear

y = 2x + 3

Linear

y = 5

Linear

y = x

Nonlinear

y=x^2

What is the domain and range of the following relation? Is it a function? {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}

Yes, it is a function. Domain: 1, 2, 3, 4, 5 Range: 1, 2, 5, 10, 15

Is this relation a function? If not, explain why. (10,1) (11,6) (12,11) (13,16)(14,21)

Yes, this relation is a function because every input has exactly one output.

Is this relation a function? If not, explain why. (0,1) (1,2) (2,3) (3,4) (4,4)

Yes, this relation is a function because every x-value has only one y-value

y = $12x

You earn twelve dollars for every lawn you cut.

Y= $0.50x + 20

Your cell phone company charges $20 a month and 50 cents per text

table

a LIST of x-values and their corresponding y-values

function

a RULE that changes one input (x) into one output (y)

function

a relation in which for every input there is exactly one output (for every x there is just one y)

definition of function

a relation that assigns exactly one output value for each input value

definition of relation

a set of pairs of input and output values

input

a specific x-value

output

a specific y-value

mapping diagram

a way to show a relation between 2 variables, aside from a graph

relation

any set of ordered pairs (x, y)

Express the relation as a table and a graph. Then state the domain and range {(4, −2), (−1, 1), (2, −3), (3, 0)}

domain: {-1, 2, 3, 4} range:{-3, -2, 0, 1}

Express the relation as a table and a graph. Then state the domain and range. {(3, −4), (2, 0), (−4, −1), (0, −3)

domain: {-4, 0, 2, 3} range:{-4, -3, -1, 0}

Express the relation as a table and a graph. Then state the domain and range {(3, 4), (1, −2), (4, −1), (2, 2)}

domain: {1, 2, 3, 4} range:{-2, -1, 2, 4}


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