Absolute Values MX1 (2 Viewers)

[the_matrix]

Hello!

So I have this horrible maths teacher who thinks everyone goes to superior tuition centres and teaches absolute values in an extremely broad way. I understand the basics of abs like |-x| = x but could anyone give me notes on how to solve absolute equations both algebraically and graphically and elaborate on 'cases'

E.g. Solve ||x-4| - 1| if x <4

Solve and then graph y = |x-2| + |x+1|


Cheers

 

[turntaker]

I don't have any notes on that sorry maybe check the resource section

Cases mean that you have to account for the negative sign. For example if an equation has an absolute value in it you don't know whether that term was positive or negative. There are several ways so solve it. You can square the terms or you can solve 2 separate equation one with minus one with plus.

I'm sure carrot stick has a better explanation but I hope it helps some what. You should go on khan academy btw

 

[Drsoccerball]

Hello!

So I have this horrible maths teacher who thinks everyone goes to superior tuition centres and teaches absolute values in an extremely broad way. I understand the basics of abs like |-x| = x but could anyone give me notes on how to solve absolute equations both algebraically and graphically and elaborate on 'cases'

E.g. Solve ||x-4| - 1| if x <4

Solve and then graph y = |x-2| + |x+1|


Cheers

You'll never get asked in any exam besides extension 2 to sketch that but if you want to know how to sketch it that bad you sketch each graph seperatly and the y coordinates of each graph to get the resulting graph

 

[braintic]

You'll never get asked in any exam besides extension 2 to sketch that

Really? We stick one of those in our year 11 Ext 1 exams every year.

 

[Drsoccerball]

Really? We stick one of those in our year 11 Ext 1 exams every year.

never seen one out of the extension 2 course

 

[braintic]

never seen one out of the extension 2 course

That's a bit different to saying you'll never be asked this. No-one had ever seen a question combining Circular Motion and Conics until 2 years ago. As long as the piecewise definition of absolute value is in, this is definitely a possibility in an exam.

 

[4025808]

You can be assessed on this sort of material in an exam, depending on your teacher's preference of question types.

If it's on the syllabus then it's potentially assessable. Would highly suggest looking at the Year 11 3U Cambridge textbook as a reference for one of those questions.

 

[4025808]

But to answer the latter question, what I just did for:

y = |x-2| + |x+1|

Is to consider the points x = 2 and x = -1, as those points are the points where the graph can change in gradient. Thankfully |x-2| and |x+1| itself represents straight lines, so drawing this shouldn't be too bad.

When x = 2, y = 3. When x = -1, y =3. Plot those points out and then draw a straight line connecting the two dots together.

Then check to the left:, i.e. sub x = -2 to get y = 5. From there use a rule to draw a straight line connecting (-1, 3) and (-2, 5) and all the way to infinity.

Then check to the right: sub x = 3 to get y = 5. Then use a ruler to draw a straight line connecting (2, 3) and (3, 5) and all the way to infinity.

You should get the shape of the graph right away.

 

[integral95]

never seen one out of the extension 2 course

2013 3u hsc :d