– WE WANT TO DETERMINE

THE DOMAIN AND RANGE OF A FUNCTION GIVEN

THE GRAPH OF THE FUNCTION. A DOMAIN IS A SET

OF ALL POSSIBLE X VALUES FOR THE FUNCTION,

AND THE RANGE IS A SET OF ALL POSSIBLE

Y VALUES FOR THE FUNCTION. WELL, X VALUES ARE ALONG

THE HORIZONTAL AXIS, AND Y VALUES ARE ALONG

THE VERTICAL AXIS. SO TO HELP US DETERMINE THE

DOMAIN OF THIS FUNCTION, WE WANT TO PROJECT THIS FUNCTION

ONTO THE X AXIS OR ANALYZE IT TO DETERMINE HOW THE GRAPH

BEHAVES FROM LEFT TO RIGHT. SO IF WE WERE TO PROJECT

THIS FUNCTION ON TO THE X AXIS, OR IF WE HAD A BRIGHT LIGHT

UP HERE THAT WAS SHINING DOWN ON THE FUNCTION, IT WOULD

PRODUCE A SHADOW ON THE X AXIS FROM -2 TO +4. BUT NOTICE HOW WE HAVE

AN OPEN POINT HERE AT X=-2, SO IT WOULD NOT INCLUDE

THE VALUE OF -2. SO WE’LL MAKE

AN OPEN POINT THERE. BUT BECAUSE THIS POINT

IS CLOSED, IT WOULD INCLUDE +4. SO THE DOMAIN OF THIS FUNCTION

WOULD BE THE INTERVAL FROM -2 TO +4 NOT INCLUDING -2,

BUT INCLUDING +4. AND WE CAN EXPRESS

THIS A COUPLE WAYS. USING INEQUALITIES WE CAN SAY

X IS GREATER THAN -2 AND LESS THAN OR=TO 4. OR IF WE WANT TO EXPRESS

THIS USING INTERVAL NOTATION, IT WOULD BE THE INTERVAL

FROM -2 TO +4 WHERE IT’S CLOSED ON +4 OR INCLUDES +4,

SO WE MAKE A BRACKET. AND IT’S OPEN ON -2, SO WE USE

A ROUNDED PARENTHESIS HERE. NOW FOR THE RANGE, WE’RE GOING

TO DO THE SAME TYPE OF ANALYSIS BUT NOW WE WANT TO PROJECT

THE FUNCTION ONTO THE Y AXIS OR ANALYZE THE GRAPH

TO DETERMINE HOW IT BEHAVES VERTICALLY. THE LOWEST POINT ON THIS GRAPH

WOULD BE RIGHT HERE AT Y=0. AND THEN NOTICE HOW IT EXTEND

ALL THE WAY UP TO Y=+8. AND IN THIS CASE

IT DOES INCLUDE 0 AND IT ALSO INCLUDES +8,

SO THE RANGE WOULD BE THE CLOSED INTERVAL FROM 0 TO 8. AGAIN, WE’RE GOING TO EXPRESS

THIS USING INEQUALITIES AS Y IS GREATER THAN OR=TO 0

AND LESS THAN OR=TO 8. OR USING INTERVAL NOTATION,

WE HAVE THE INTERVAL FROM 0 TO 8,

AND IT’S CLOSED BOTH ON 0 AND 8

BECAUSE IT WOULD INCLUDE THE ENDPOINTS. NOW LET’S TAKE A LOOK

AT ANOTHER EXAMPLE. AGAIN, WE’LL FIRST TRY

TO DETERMINE THE DOMAIN, WHICH IS THE SET

OF ALL POSSIBLE X VALUES, AND X VALUES ARE ALONG

THE HORIZONTAL AXIS. SO WE WANT TO PROJECT

THIS FUNCTION ONTO THE X AXIS OR ANALYZE IT TO DETERMINE

HOW IT BEHAVES MOVING FROM LEFT TO RIGHT. WELL, THE LEFT MOST POINT

ON THIS GRAPH WOULD BE RIGHT HERE AT X=-2,

AND THEN IT WOULD INCLUDE EVERY X VALUE

ALL THE WAY OUT TO +2. BUT NOTICE HOW WE HAVE

AN OPEN POINT RIGHT HERE AT X=2, SO IT DOES

NOT INCLUDE +2, SO IT’S AN OPEN POINT HERE. IT DOES INCLUDE THIS POINT HERE,

SO IT’S CLOSED HERE. SO THE DOMAIN

WOULD BE THE INTERVAL FROM -2 TO 2 INCLUDING -2,

AND NOT INCLUDING 2. SO WE COULD SAY

X IS GREATER THAN OR=TO -2 AND LESS THAN +2,

OR USING INTERVAL NOTATION, WE HAVE THE INTERVAL

FROM -2 TO 2, CLOSED ON -2 AND OPEN ON 2. NOW, TO DETERMINE THE RANGE,

WE WANT TO PROJECT THE FUNCTION ONTO THE Y AXIS

OR THE VERTICAL AXIS, OR ANALYZE

THE FUNCTION TO SEE HOW IT BEHAVES VERTICALLY. THE LOWEST POINT ON THIS GRAPH

WOULD BE RIGHT HERE AT Y=-4. NOTICE HOW IT WOULD INCLUDE -4

BECAUSE THIS POINT IS CLOSED. AND THEN THE GRAPH

INCLUDES EVERY Y VALUE ALL THE WAY UP TO +4,

NOT INCLUDING +4 AGAIN BECAUSE

OF THIS OPEN POINT. SO THE RANGE WOULD BE

THE INTERVAL FROM -4 TO 4, INCLUDING -4

BUT NOT INCLUDING +4. SO WE’D HAVE

Y IS GREATER THAN OR=TO -4 AND LESS THAN 4. USING INEQUALITIES OR USING

INTERVAL NOTATION FROM -4 TO 4, OPEN ON 4, AND CLOSED ON -4. OKAY. I HOPE YOU FOUND

THESE TWO EXAMPLES HELPFUL. WE’LL TAKE A LOOK

AT TWO MORE IN THE NEXT VIDEO.

## 29 Comments

## W Slater

You have saved my life. Thank you!

## Matthew Santner

yes you explain very well thanks.

## melanee cuneapen

I still don't get it…..

## I am Alex

i have no idea what i just watched

## Timi

Thanks it's easy now

## Elvis Nahum

cool i actually got it…not bad

## peter essa

Really helpful

## MyThiK Clan

wow i wished i got this im a senior and i have to pass this for homeschool hope i dont fail

š

## DJ AD

what does he mean "not including"……im confused

## DJ AD

….what happens if you fail homeschool??

## DJ AD

O āopen

Closed is the colored in dot

## MyThiK Clan

Have to take that one class all over again

## NorCal Gunner

Thanks, it help me

## UaruGaming

thank you.

you replaced my shitty math teacher

## Silverinvestor2020

Thanks not as boring as being at school

## fluffy snowcone

Thank you!

## Oh Tay

How do you know

What signs to use, I'm using hawks learning system & it doesn't show open or closed

## Zekarias Araya

Thank you.

## Rebecca Dixon

THANK YOU!

## sameolhim

this helped a lot, the only problem is the captions are in the way at times but this really helped!

## valerie Garcia

wouldn't the range be negative infinity to positive infinity because they are all real numbers

## mike hawks

Your awesome thanks!

## Pearl Watson

THANK YOU, because this is the only video that explains what my child is doing in class: being able to determine the inequality sentence from looking at a graph. Thanks for showing the numbers on the graph, using different colors, writing the inequality, and listing the domain & range. Writing the inequality on the left side is like writing the sign backwards.

## Evander Ali

But how do I determine the inequality signs?

## Myra Al

really bad not clear AT all

## Luis Ordaz

Thanks bro!

## DeathAngel

Doesn't make sense using opened and closed. Unsure when you use them.

## Divine Umutoni

Thank you somuch

## Beado Bear

Your voice makes me want to kill my self