Function Review
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}
