A Quick Pause For Modulus Func-tionnn

Question 1

If an inequality is of the form mod x-a <b how can you write this

Where does it come from

Answer 1

Can write this like -b <x-a<b and then add a both side to give -b+a<x<a +b

Comes from solving a simple inequality mod x <1, you’ll see you end up getting that range so itsnot directly obvious but this is Ei thing you NEED TO KNOW

Question 2

Okay if inequality is z<x<y how to convert into mod form?

Answer 2

Add y +z /2 that gives you a

Then subtrsvt a from one side or add from another should fall to same number

Question 3

IMPORTSNT how to convert from inequality to mod form EXACT STEPS NO MATTER WHAT

Answer 3

add both extreme and divide by 2 EVEN IF THEY ARE NEGATIVE

Whatever you get, that is = to a!
So even if - number, becomes x - -a = x+a in the modulus!

NOW take number and SUBTRACT FROM BITH SIDES (keeping sign), should end up in the SAME number and can not comolete it

Question 4

How to solve mod inequalities on both sides easy way but what to do

Answer 4

Can draw graoh long

Easy is to sqaure and eauate, but then MUST check if these answers actually fit

Question 5

And what if the inequalities have a mod + a CONSTSNT, can you still sqaure?

How do you draw graphs (watch out for?)

Answer 5

In this case no you Cant sqaure , as it doesn’t achieve anything

Here you must use graphs! Draw new graph based on intercept changes and equate as it won’t just be +- the mod

Question 6

Can you multiply and divide equations wholey with modulus?

Answer 6

YES YOU CAN, but only multiply and divide

Question 7

How to draw mod growths with a transformation?

Answer 7

It’s same as complete sqaure form to find vertex

Then must pally transformation to both + - graohs

Draw groans
Find intercelts

Might have to reflect

Or just draw it normally then do trandfosmtion