– WE WANT TO DETERMINE

THE DOMAIN AND RANGE OF THE FUNCTION F(X)=

THE ABSOLUTE VALUE OF X + 2 – 3. THE DOMAIN CONSISTS

OF ALL POSSIBLE INPUTS OR X VALUES FOR THE FUNCTION

AND THE RANGE CONSISTS OF ALL POSSIBLE OUTPUTS

OR Y VALUES FOR THE FUNCTION. NOW THERE ARE A COUPLE

OF WAYS OF DETERMINING THE DOMAIN AND RANGE. WE COULD USE WHAT WE KNOW

ABOUT THE PROPERTIES OF THE ABSOLUTE VALUE FUNCTION

TO DETERMINE THE DOMAIN AND RANGE OR WE COULD

ALSO MAKE A GRAPH OF THE FUNCTION

AND ANALYZE THE GRAPH. LET’S START

BY ANALYZING THE GRAPH. SO THE FIRST STEP

WOULD BE TO EITHER MAKE A T-TABLE OR USE TECHNOLOGY

TO CREATE THE GRAPH PROVIDED HERE. ONCE WE HAVE THE GRAPH,

WE CAN ANALYZE THE BEHAVIOR OF THE FUNCTION HORIZONTALLY

AND VERTICALLY TO HELP DETERMINE THE DOMAIN AND THE RANGE. WHAT I MEAN BY THAT IS,

TO DETERMINE THE DOMAIN, IF WE WERE TO PROJECT

THIS FUNCTION ONTO THE X-AXIS, NOTICE HOW IT INCLUDES

THE ENTIRE X-AXIS. ANOTHER WAY TO THINK OF THIS IS,

THE GRAPH CONTINUES TO THE RIGHT AND CONTINUES TO THE LEFT

INDEFINITELY WITHOUT ANY HOLES OR BREAKS. SO THE DOMAIN APPROACH

IS POSITIVE INFINITY TO THE RIGHT

AND NEGATIVE INFINITY TO THE LEFT. THEREFORE, THE DOMAIN

OF THIS FUNCTION WOULD BE ALL REAL NUMBERS. OR IF WE WANTED

TO USE INTERVAL NOTATION, WE COULD USE THE INTERVAL

FROM NEGATIVE INFINITY TO POSITIVE INFINITY. NOW TO DETERMINE THE RANGE,

WE’D HAVE TO PROJECT THE GRAPH ONTO THE Y-AXIS

OR DETERMINE HOW THE GRAPH BEHAVES VERTICALLY. NOTICE HOW THE LOWEST POINT

ON THE GRAPH IS THIS POINT HERE WITH A Y VALUE OF -3. AND THEN FROM HERE, OF COURSE,

THE GRAPH IS MOVING TO THE RIGHT AND LEFT VERY QUICKLY,

BUT NOTICE HOW IT’S ALSO MOVING UPWARD. SO IF WE PROJECTED THIS GRAPH

ONTO THE Y-AXIS, IT WOULD ACTUALLY APPROACH

POSITIVE INFINITY ALONG THE Y-AXIS,

WHICH MEANS THE RANGE WOULD BE FROM -3

TO POSITIVE INFINITY AND IT DOES INCLUDE -3. SO WE CAN SAY THE RANGE

IS GREATER THAN OR EQUAL TO -3. OR USING INTERVAL NOTATION,

IT WOULD BE THE INTERVAL FROM -3 TO INFINITY

AND IT’S CLOSED ON -3 BECAUSE IT DOES INCLUDE -3. NOW IF WE DIDN’T WANT TO MAKE

A GRAPH AND WE KNEW A LOT ABOUT THE PROPERTIES

OF THE ABSOLUTE VALUE FUNCTION, WE COULD USE REASONING

TO DETERMINE THE DOMAIN AND RANGE. WHAT I MEAN BY THAT IS,

WE COULD THINK TO OURSELVES WHAT ARE THE POSSIBLE VALUES

OF X THAT WE COULD USE TO SUBSTITUTE IN HERE

AND THEN EVALUATE THE FUNCTION? AND THE ANSWER IS,

WE COULD USE ANY REAL NUMBER HERE,

ADD 2 TO IT, TAKE THE ABSOLUTE VALUE

AND THEN SUBTRACT 3. AND THAT’S THE REASON WHY

OUR DOMAIN IS ALL REAL NUMBERS. AND THEN FOR THE RANGE,

IF WE KNEW THE ABSOLUTE VALUE OF A NUMBER IS ALWAYS

GOING TO BE>THAN OR=TO 0, WELL,

THIS IS ALWAYS>THAN OR=TO 0

AND THEN WE SUBTRACT 3, THEN THE FUNCTION VALUE,

OR Y VALUE, IS ALWAYS GOING TO BE>THAN

OR=TO -3. AGAIN, IF THIS VALUE RIGHT HERE

IS ALWAYS GOING TO BE 0 OR SOME POSITIVE NUMBER,

THEN THE FUNCTION VALUE. OR Y VALUE, MUST ALWAYS

BE>THAN OR=TO -3 WHICH IS OUR RANGE. SO I KNOW IT CAN BE CHALLENGING

TO JUST THINK ABOUT WHAT THE DOMAIN AND RANGE

WOULD BE, GIVEN THE FUNCTION. SO I THINK IT’S ALWAYS HELPFUL

TO SKETCH A GRAPH OF THE FUNCTION

AND ANALYZE THE GRAPH, IF NOTHING ELSE,

JUST TO VERIFY THE DOMAIN AND RANGE.

## 8 Comments

## Scott Johnson

thank you so much man! ðŸ˜€

## Carl Mirita

Awesome! Better then my teacher! It always seems like teachers do worse when they have a class then over the internet. It's probably because their more relaxed or something.

## asian boba

thankyou so much!

## SummativeWritting

This video is bad and you should feel bad.

## timelordvictorious96

thanks a lot! this really helped

## Caleb Stern

or… you suck at math.

## SummativeWritting

Well, the reason I feel this video is bad is because it took "bullcleo1" 3:45 to go over perhaps the easiest example of an absolute value function. The only person this would help is someone who didn't know the definition of the domain and/or range or perhaps someone who doesn't know how to graph an absolute value function. I think the person who this video helps is bad at math. ðŸ˜›

## Allyson

Anyone who says that this video was "bad" or "stupid" needs to, in my opinion, keep their mouths shut. Not everyone can look at a math problem and learn how to do it in a mere moment. For some, it takes "Oh, right! Now I remember!" to actually get a new lesson. It is VERY rude to insult people on the way, or pace, at which they learn. If you can remember it and don't need any reminding or pointers, good for you, as for making the assumption that everyone else who needs a little reminding is "bad at math", well, that is strictly impossible to prove true, and it is a very not-well-thought-out remark. Keep your opinion-based, rude comments to yourself.