hello John Zimmerman with tabla class

comm here to help you out with functions

and relations so probably targeted at

those middle and high school students

and no I don't know pre-algebra algebra

1 algebra 2 and Beyond you're going to

be studying this topic of functions huge

topic in math and one of the initial

things that you have to do one of the

tasks that you have to be able to do is

determine whether a relation is a

function now you know I'm using terms

and you know names like relations and

functions and ah this is going to be a

short little video

you can't possibly you know I'm teach

you everything there if you need more

information on those topics you really

need to learn it come on a tablet class

comm which will get you squared away so

let's just focus in on the question to

to determine whether a given relation is

a function okay so here is an example of

relation and a relation in math a

relation a relation excuse me in math

kind of think of it as kind of a

collection of points so here I have a

bunch of XY points

okay all I'm going to demonstrate this

encumber different couple of different

ways or I can't talk today anyway so I

have a collection of points and in its

most basic sense this would represent a

relation so how do we know whether a

relation is a function I want to show

you a couple easy ways to think of it

okay what we want to look at is the

mapping okay from UM we want to

associate each X with its respective Y

now of course we already have that here

in these ordered pairs but I'm going to

do it this way

okay it's kind of mapping diagram some

of you or maybe all of you are familiar

with this and the way we constructed is

we take a point let's say like 1 3 it's

going to be 1 I'm going to put the X

here and then we're going to put the 3

here then we're going to draw an arrow

from the X to the Y like so ok so that's

1 2 3 and here this would be 4 2 7 and

then we have negative 2 to 6 and 2 to 9

ok so

a mapping diagram and I simply you know

did this here is it another way to

illustrate this same relationship same

relation excuse me because I think is

just easier to show you whether or how

to test a particular relation to see if

it's a function or not okay here's the

whole idea alright just make it simple

for each x-value okay each x-value can

only go to one and only one y value okay

so i'll state that again for I'll state

that again for each x value it can only

point to one Y value so for each x value

can only point to one Y value so in this

case here this collection of points

represents and it does in fact represent

a function okay so this is a relation

and it's also a function y because each

X is pointing to one only one y value

okay so now let's mess this thing up

want to go ahead and show you a couple

different examples so let's say you

build these mapping diagrams you can get

like let's say 1 2 3 4 5 ok so I'm just

going to start doing some things like

this now let me ask you this question is

this mapping diagram of a relation is it

a function and remember each X can only

point to one Y so hopefully you answered

it correctly in fact this is a function

this relation is a function ok 1 points

2 4 and only for 2 points 2 4 and only

for now here this might have messed you

up even like oh wait it's pointing to

the same wine no that's ok as long as

the x value is going to one and only one

y value it's alright and of course three

points to five okay so this is a

function let me show you another

situation that might confuse you one

three five six nine seven okay

all right how about this

okay now is this a function right one

points to six that's good now three is

trying to point to nine and seven at the

same time so this is where we have

problems okay so this relation can I

remember these are just collection of

points this would represent the point

one six this would represent the point

three nine this is represent the point

three seven and then five seven okay so

when we plot of these or put these into

a mapping diagram we can clearly see

that it fails the test to be a function

okay now there's other ways you could do

that you can look and see here that we

have the same X with different Y values

I'll depend on how your teacher teaches

you okay I think this is an easy way of

looking at it

alright kind of stay within the topic

but switch gears on you and talk about

the vertical line test it's another way

to determine whether something is a

function okay whether relation is a

function excuse me and the way it works

is this alright if you can draw a

vertical line through the graph of a

relation a vertical line and it only

crosses through that graph once okay so

I drew a vertical line here crap you're

gonna cross through once once once

anywhere along the scrap where I could

draw a vertical line if it can only

cross to that graph one time guess what

it is a function okay so in this case

this particular graph would represent a

function R this relation the graph of

this relation to be more specific would

represent a function so to look at a

counter example let's look at something

like this alright let's maybe look at

look at a circle okay so a circle would

fail the vertical line test because it

passes through a vertical line passes

through the graph twice okay so that

fails so this is a relation alright so x

squared plus you know I'm not even going

to do that I was going to start writing

the equation recirc 'old

need to just stick with topic on hand so

if you're given a graph of a relation

and you're asked to determine whether it

is a function just use the vertical line

test if you're given points use that

mapping diagram okay

so I've just crammed in like I don't

know three weeks worth of concepts and

stuff into like a few minute video but

listen check us out at tablet class comm

if you need help in mathematics we truly

do stress or strive clear and

understandable way we explain math we

don't teach it to you in ways that you

know your average or your you know

real-life teenagers you know think okay

and of course if you're in college we

can help you out we have to do day free

trial we know we can help you so anyways

hope this video helped and good luck to

yourself