Is it a function?

given the relation {(-4,-2),(1,-4),(3,0),(4,3)} determine if this relation is a function
a. yes it is a function because each x value has only one y value
b. no it is not a function because -4 appears twice
c. no it is not a function because each x value does not have a unique y value
d. yes it is a function because each x value is unique

by definition of a function:
a. yes it is a function because each x value has only one y value

Decide whether the relation defines a function.

Decide whether the relation defines a function.
{( -3,  3), ( -1,  -1), ( 3,  -5), (13,  2)}

Solution:

We check that every element in the domain (the set of all first coordinates) corresponds to only one element of the range (the set of all second coordinates). For this relation the answer is yes, so this relation is a function

Exactly what is the vertical line test?

It is a way to check if a graphed relation is a function. If a vertical line can intersect a graph in more than one place that means that there is more than one vertical coordinate for at least one horizontal coordinate. This contradicts the definition of a function.

C = {(1/2, 5), (-3, 7), (3/2, 5), (1/2, -1)} What are the domain and range of each relation? Is the relation a function?

domC={1/2, -3, 3/2}
ranC={5, 7, -1} 
not a function, 1/2 is mapped to two different numbers

Give the domain and range of G. Write your answers using set notation

Suppose that the relation is defined as follows. {(5,5),(8,0),(6,-2),(-9,-8)} Give the domain and range of G. Write your answers using set notation

G={(5,5),(8,0),(6,-2),(-9,-8)}
The domain is the set of x-coordinates and the range is the set of y-coordinates:

dom(G)={5,8,6,-9}
ran(G)={5,0,-2,-8}

:)

determine if each relation is a function

a. y=-3x-6 b. x=0 c. {(2,7),(5,-2),(7,0),5,-2)} d. y=5 e. {(0,6),(-3,6)(-6,6)} f. {(5,1),(4,-3),(3,7),(0,5) thank you!!

Your Answer:

a) yes - all non-vertical lines are functions
b) no - this is a vertical line
c) no - this set is not even a relation, two elements are not ordered pairs
d) yes (see a) )
e) yes - every x-coordinate is matched with exactly one y-coordinate in this relation

:)

Find the domain and range.

Find the domain and range.
R={( -4, -7), ( 12, 5), ( 11, -9), ( 11, -3)}


Solution:

The domain of a relation is the set of all first coordinates so we can write Dom R={-4, 12, 11}

The range of a relation is the set of all second coordinates so we can write Ran R={-7, 5, -9, -3}