– WE WANT TO DETERMINE

THE DOMAIN AND RANGE OF A FUNCTION GIVEN

THE GRAPH OF THE FUNCTION. THE DOMAIN IS A SET

OF ALL POSSIBLE X VALUES OF THE FUNCTION. X VALUES OCCUR

ALONG THE X AXIS OR THE HORIZONTAL AXIS. AND THE RANGE IS A SET

OF ALL POSSIBLE Y VALUES OF THE FUNCTION,

AND Y VALUES OCCUR ALONG THE VERTICAL AXIS. SO IF WE’RE GIVEN

THE GRAPH OF A FUNCTION, AND WE WANT TO DETERMINE

THE DOMAIN OF THE FUNCTION, WE WANT TO PROJECT THE GRAPH

ONTO THE X AXIS, OR DETERMINE HOW THE GRAPH BEHAVES

HORIZONTALLY ALONG THE X AXIS. WHAT I MEANT BY THAT IS NOTICE

HOW THE LEFT MOST POINT OF THIS GRAPH OCCURS RIGHT HERE

WHEN X IS APPROACHING -3. AND THE RIGHT MOST POINT

ON THE GRAPH WOULD BE HERE WHEN X IS EQUAL TO +2. AND THE GRAPH WOULD ALSO CONTAIN

EVERY X VALUE BETWEEN -3 AND 2. BUT THERE’S

ONE MORE THING WE NEED TO BE CAREFUL

ABOUT HERE, -3 IS NOT GOING TO BE

IN THE DOMAIN OF THIS FUNCTION BECAUSE OF THIS OPEN POINT HERE. SO LETS MAKE AN OPEN POINT

HERE TO INDICATE THAT. BUT NOTICE THAT X=2,

THIS POINT IS CLOSED, SO IT WOULD INCLUDE +2. SO THE DOMAIN OF THIS FUNCTION

IS GOING TO BE FROM -3 TO +2, NOT INCLUDING -3

BUT INCLUDING +2. SO IF WE WANTED TO EXPRESS

THIS USING INEQUALITIES, WE WOULD SAY

X IS GREATER THAN -3 AND LESS THAN OR EQUAL TO +2. IF WE WANT TO USE

INTERVAL NOTATION, THE INTERVAL’S FROM -3 TO 2. IT INCLUDES 2

SO IT’S CLOSED ON 2, SO WE USE THIS SQUARE BRACKET. AND IT’S OPEN ON -3

BECAUSE IT DOES NOT INCLUDE -3, SO WE USE A ROUNDED PARENTHESIS. THESE TWO MEAN THE SAME THING. AND THEN TO DETERMINE THE RANGE,

WE NOW WANT TO PROJECT THIS FUNCTION

ONTO THE Y AXIS, OR DETERMINE

HOW IT BEHAVES VERTICALLY. SO, AGAIN, NOTICE

HOW THE LOWEST POINT ON THIS GRAPH HERE

IS APPROACHING -5, AND THEN IT INCLUDES

EVERY Y VALUE ALL THE WAY UP TO

THIS HIGH POINT WHEN Y IS +5. BUT NOTICE HOW IT’S NOT GOING

TO INCLUDE -5 BECAUSE OF THIS OPEN POINT,

BUT IT WILL INCLUDE +5 BECAUSE OF THIS CLOSED POINT. SO THE RANGE IS GOING

TO BE FROM -5 TO +5, NOT INCLUDING -5

AND INCLUDING 5. SO WE CAN SAY

Y IS GREATER THAN -5 AND LESS THAN OR EQUAL TO +5. OR USING INTERVAL NOTATION

SQUARE BRACKET FOR 5 BECAUSE IT INCLUDES 5,

AND A ROUNDED PARENTHESIS FOR -5 BECAUSE IT DOES NOT INCLUDE -5. NOW LET’S GO AND TAKE A LOOK

AT A SECOND EXAMPLE. WE’LL START BY DETERMINING

THE DOMAIN. SO WE WANT TO PROJECT

THIS FUNCTION ON TO THE X AXIS, OR DETERMINE

HOW IT BEHAVES HORIZONTALLY. WELL, THE LEFT MOST POINT OCCURS

RIGHT HERE AT X=-4, AND THEN NOTICE HOW THE GRAPH

MOVED TO THE RIGHT INDEFINITELY BECAUSE WE ARE ASSUMING

THIS GRAPH IS GOING TO CONTINUE IN THIS DIRECTION. SO THE DOMAIN

WOULD START AT -4 AND THEN MOVE

TO THE RIGHT INDEFINITELY, MEANING IT’S GOING TO APPROACH

POSITIVE INFINITY. SO THE DOMAIN

WOULD BE X IS GREATER THAN OR EQUAL TO -4,

OR USING INTERVAL NOTATION WE HAVE INTERVAL

FROM -4 TO INFINITY. IT INCLUDES -4

SO WE HAVE A BRACKET. AND THEN FOR INFINITY

WE ALWAYS USE A ROUNDED PARENTHESIS. AND THEN FOR THE RANGE,

WE WANT TO PROJECT THIS FUNCTION

ONTO THE Y AXIS, OR DETERMINE

HOW IT BEHAVES VERTICALLY. SO THE LOWEST POINT

ON THIS GRAPH IS RIGHT HERE AT Y=-4. THIS IS A CLOSED POINT

SO IT DOES INCLUDE -4. NOW, WHEN WE TRY TO DETERMINE

HOW HIGH THIS GRAPH GOES, WE NEED TO BE CAREFUL

BECAUSE OF COURSE IT IS MOVING TO THE RIGHT

VERY FAST, BUT NOTICE HOW IT ALSO IS MOVING UPWARD. SO EVEN THOUGH IT’S NOT SHOWING

ON THE SCREEN, THIS GRAPH WOULD CONTINUE

TO MOVE UPWARD, AND THEREFORE THE RANGE IS GOING TO APPROACH

POSITIVE INFINITY. SO THE RANGE

WOULD BE Y IS GREATER THAN OR EQUAL TO -4,

OR USING INTERVAL NOTATION, JUST LIKE FOR THE DOMAIN,

IT WOULD BE CLOSED ON -4 TO POSITIVE INFINITY. OKAY. SO I HOPE

THESE TWO EXAMPLES WERE HELPFUL.

## 14 Comments

## Maxine Williams

This was so helpful!!!!! =)

## Emily Nguyen

FINALLY what I was looking for! ๐ awesome job explaining

## Anita

OMM THANK YOU SO MUCH YOU HAVE JUST MADE MY LIFE SO MUCH EASIER I LOVE YOUUUUU

## Liv Burows

Holy Crap! Everything just clicked. Thank you sooooooo much

## kittylove199

thank you so much!!! I Have exam today at 9, and the only thing i didn't get was the domain and the range, this really helped!!! thanks again!!!!

## Brittany Skouson

thank you for the video!!! Made lots of notes this video was awesome..

## TechWiz49

Thanks a lot! very clear helps so much!

## jepoy canlapan

how will I know if it's greater than or less than?ย

## Eric Morales

very helpful…both videos

## April Alfaro

question?? I am confused. first function at 1:30 m you said x greater thanย -3 but the symbol says less than??

## okrabasil32

At 2:45 you write -5 < y but it should be -5 > y

## Juanita Adanza

i like this video for my ESOl class

## Maxine Adams

thank God I found this video, got a major test tomorrow

## Te' G

So glad I found this๐๐๐…Had to find this vid through my Youtube app. For some reason I can't watch videos on myopenmath on my LG.