– WE WANT TO DETERMINE

WHICH OF THE FOLLOWING TABLES REPRESENT FUNCTIONS. A FUNCTION IS RELATION

IN WHICH EVERY INPUT HAS EXACTLY ONE OUTPUT. SO LOOKING AT THESE TABLES,

THE X VALUES WILL BE THE INPUTS AND THE Y VALUES

WILL BE THE OUTPUTS. SO IF THESE TABLES

ARE FUNCTIONS, WE COULD SAY

THAT EVERY X VALUE MUST HAVE EXACTLY ONE

CORRESPONDING Y VALUE. IF THIS IS NOT TRUE,

THE TABLE WOULD NOT BE A FUNCTION. SO WE WANT TO ANALYZE

THESE TABLES AND MAKE SURE EVERY X VALUE HAS EXACTLY ONE

CORRESPONDING Y VALUE. SO WE TAKE A LOOK

AT THIS FIRST TABLE, NOTICE THAT THE INPUT

OF 2 OCCURS TWICE WITH TWO DIFFERENT OUTPUTS. HERE WE HAVE AN INPUT OF 2

WITH AN OUTPUT OF 3, AND HERE WE HAVE AN INPUT OF 2

WITH AN OUTPUT OF -1. THIS DOES NOT SATISFY

THE DEFINITION OF A FUNCTION BECAUSE THE X VALUE OF 2

ACTUALLY HAS TWO DIFFERENT OUTPUTS, OR TWO

CORRESPONDING Y VALUES. THEREFORE, THIS

WOULD NOT BE A FUNCTION. TO HELP VISUALIZE THIS

IT’S OFTEN HELPFUL TO SHOW THE RELATIONSHIP

BETWEEN X AND Y USING MAPPING, WHICH MEANS

YOU PUT THE SET OF INPUTS HERE OR THE DOMAIN HERE,

AND THE SET OF OUTPUTS OR THE RANGE HERE,

AND THEN DRAW ARROWS TO SHOW EACH INPUT

WITH THE CORRESPONDING OUTPUT. SO NOTICE OUR INPUTS

WOULD BE 2, -1 -4, AND 5. WE WOULD NOT LIST 2 TWICE,

SO WE HAVE 2, -1, -4, AND 5. AND THE OUTPUTS

ARE THE Y VALUES, SO WE HAVE 3, 4, 0, -1, AND 7. SO WHEN THE INPUT IS 2,

HERE THE OUTPUT IS 3. SO WE SHOW THAT RELATIONSHIP

BY DRAWING AN ARROW FROM 2 TO 3. WHEN THE INPUT IS -1

THE OUTPUT IS 4. AND WE’LL OFTEN SAY

-1 MAPS TO 4, SO WE CAN SAY -4 MAPS TO 0. BUT NOTICE HOW 2

ALSO MAPS TO -1, SO WE’D DRAW ANOTHER ARROW

FROM 2 TO -1, AND THEN 5 MAPS TO 7. SO NOTICE THAT 2

HAS TWO OUTPUTS, ONE HERE AND ONE HERE. AND THIS IS THE REASON

WHY THIS IS NOT A FUNCTION. NOW LETS TAKE A LOOK

AT THE SECOND TABLE. NOTICE THAT NONE OF THE INPUTS

HERE REPEAT THEMSELVES, THEREFORE THERE’S NO WAY

EVERY X CAN HAVE MORE THAN ONE CORRESPONDING Y VALUE. SO THIS WILL BE A FUNCTION,

BUT WE’LL ALSO MAP IT TO ILLUSTRATE IT BETTER. SO, AGAIN, WE’LL PUT THE INPUTS

OR THE ELEMENTS OR NUMBERS IN THE DOMAIN HERE,

AND THEN WE’LL PUT THE ELEMENTS OR THE NUMBERS

AND THE RANGE HERE. SO THE INPUTS WOULD BE 4, -3, 1,

2, 5, AND NOTICE THERE IS SOME REPETITION IN THE OUTPUTS. THERE’S ONLY THREE OUTPUTS,

-5, -2, AND 0. NOW LET’S GO AHEAD

AND SHOW THE MAPPING. IF AN INPUT OF 4

THE OUTPUT IS -5, SO 4 MAPS TO -5,

-3 MAPS TO -2, 1 ALSO MAPS TO -2,

2 ALSO MAPS TO -2, AND 5 MAPS TO 0. NOW, THIS DOES LOOK STRANGE

BECAUSE WE HAVE THREE ARROWS ALL POINTING TO -2 IN THE RANGE,

BUT NOTICE HOW EVERY INPUT OR EVERY VALUE HERE

DOES HAVE EXACTLY ONE OUTPUT, EVEN THOUGH AT TIMES

THEY DO HAVE THE SAME OUTPUT. SO BECAUSE EVERY X

HAS EXACTLY ONE Y THIS IS A FUNCTION. NOW LET’S TAKE A LOOK

AT ONE MORE EXAMPLE HERE. THE FIRST THING WE SHOULD NOTICE

IN THIS TABLE IS THAT THE INPUT OF -1 DOES OCCUR TWICE. SO -1 DOES HAVE TWO OUTPUTS

OR CORRESPONDING Y VALUES. THEREFORE, AGAIN,

THIS TABLE IS NOT A FUNCTION. AND LET’S GO AHEAD

AND MAP THIS AS WELL. SO THE INPUTS ARE

0, -1, 4, AND 2. AGAIN, WE DO NOT LIST -1 TWICE. AND THE OUTPUTS

WILL BE 3, 4, 0, -1, 1. SO 0 MAPS TO 3,

-1 MAPS TO 4, 4 MAPS TO 0,

2 MAPS TO -1, AND THEN -1 MAPS TO 1. SO FROM -1 WE HAVE

ANOTHER ARROW GOING FROM -1 TO +1. SO, AGAIN, BECAUSE THIS INPUT

OF -1 HAS ACTUALLY TWO OUTPUTS, THIS TABLE DOES NOT REPRESENT

A FUNCTION. I HOPE YOU FOUND

THESE EXAMPLES HELPFUL.

This helped so much! Thank you.

got it! thanks

thank you so much my teacher sucks at teaching

my teacher is so fucking annoying i asked her what we were doing that day and she said i don't care if you have that attitude at home but don't bring that into my classroom and i was like um wtf?????

Thanks!

you explained that better than my teacher

Thx m80

Thanks 🙂

What if there's a pair like (-2,-3), (-2,-3) will it be a function?

Was doing homework. This helped. Thank you!

Thank you so much 😎

U gain 1 sub

Thanks me latet

Thanks, this was really helpful it saved my homework that was supposed to be due tomorrow.

This will me so much for my notes. Thanks!

* Help

my homework answers says otherwise wtf!!

that was very helpful!

If input has a repeated number it's automatically not a function, if the input is single and does not repeat it's a function. got it, thanks a lot.

Thank youuuu

This is very helpful! Now I understand, thanks!

1:20 the not a function is a dick Lol😂😂😂

Im still confused

Note: yes im that dumb

Wow thanks this really helped I'm so grateful!!

you just saved me for not turning in my homework

thank you! i missed a day of school and this really helped me with my hw!

Homework done thx 😊

What if the X side has a Input number that is repetead but as both positive and negative???(im doomed)

Thanks