shelby1290
  • shelby1290
Determine whether the following relations are functions. Give the appropriate reason for your answer. *pictures included a) {1,3), (2,3), (3,2), (1,4), (4,1)} b) picture c)picture d)picture e)picture
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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shelby1290
  • shelby1290
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shelby1290
  • shelby1290
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anonymous
  • anonymous
if you want to know that a relation is function look at the x of every ordered pair.if you saw that one of x is repeated and their y isn't same that relation isn't a function for example : {(1,2),(1,3)} is not a function.

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anonymous
  • anonymous
for b do two arrows come out of any number?
anonymous
  • anonymous
and for d and e we use a test :vertical line test If a vertical line can be drawn that crosses two points on the graph of the relation, then the relation is not a function.
shelby1290
  • shelby1290
@amirreza1870 i see...but what if your x values aren't the same but one of y-values is repeated twice? Is that a function?
shelby1290
  • shelby1290
|dw:1442369545961:dw|
shelby1290
  • shelby1290
^like that for example
misty1212
  • misty1212
HI!!
shelby1290
  • shelby1290
@satellite73 no they don't. Does that make it a function or not a function? How about part c?
misty1212
  • misty1212
y values are unimportant for determining if it is a function or not
shelby1290
  • shelby1290
then what must I pay attention to?
anonymous
  • anonymous
since there is only one arrow out of each domain element, then it IS a function
shelby1290
  • shelby1290
I always get confused when it comes to identifying them
misty1212
  • misty1212
only pay attention to the x values if they are repeated, it is NOT a function
anonymous
  • anonymous
no a is a function but it is not one-to-one
misty1212
  • misty1212
don't fret about "one to one" yet, worry about that later
shelby1290
  • shelby1290
@amirreza1870 what's one-to-one ?
misty1212
  • misty1212
vertical|dw:1442369892767:dw| line test is easy if you have a graph
anonymous
  • anonymous
i an sorry about using one-to -one but that means a function that for every x ,y is a different number for example {(1,3),(2,3)} is function because 1 and 2 are different but it's not one-to-one because their y is same.
shelby1290
  • shelby1290
@misty1212 so part d is a function because it passes the vertical line test and doesn't go through more than one point? and part e) is not a function because it failed the vertical line test and passes through more than one point
shelby1290
  • shelby1290
@amirreza1870 okay i get that so if the x-values are different its referred to as one-to-one ?
anonymous
  • anonymous
no. if the y values are different it is a one-to-one function.the difference of x values show that relation is function
shelby1290
  • shelby1290
ahhhh okay so... one-to-one=not a function difference in x-values=function
anonymous
  • anonymous
we use this expression (one-to-one) for a function. so a relation must be a function if we want to see that is one-to-one or not
anonymous
  • anonymous
i think it's better to use a Venn diagram |dw:1442371114951:dw| as you can see only one arrow comes out of a and b so this is a function but their y is same (we said if the y was different it is one-to-one) so it is not one-to-one
shelby1290
  • shelby1290
alright that makes sense thanks for the help!

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