FP2 inequalities question

Hey guys how do I go about drawing the graph on the left hand side? (mod x/x+2)

Cheers!

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Reply 1

Kevin De Bruyne

21

Draw y = x/(x-2) and apply the modulus to the graph.

Reply 2

Plagioclase

21

Original post by iMacJack

Hey guys how do I go about drawing the graph on the left hand side? (mod x/x+2)

Cheers!

Posted from TSR Mobile

You just need to draw the ordinary graph for

\frac{x}{x+2}

and then flip any negative parts around the x axis.

Reply 3

Zacken

22

As above, draw the graph of

\frac{x}{x+2}

, note that its important features are that it has a horizontal asymptote

y=1

, a vertical one

x=-2

, passes through the origin, is only negative between

-2 < x < 0

, positive everywhere else, etc...

Reply 4

iMacJack

OP

16

Original post by SeanFM

Draw y = x/(x-2) and apply the modulus to the graph.

Gunna sound stupid but I'd rather know and sound stupid than not know and agree just to seem like I get it...

How do I go about drawing x/x+2?

If it's any consolation I've just been thrown into FP2 without having done C3/4 by my school
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Reply 5

Kevin De Bruyne

21

Original post by iMacJack

Gunna sound stupid but I'd rather know and sound stupid than not know and agree just to seem like I get it...

How do I go about drawing x/x+2?

If it's any consolation I've just been thrown into FP2 without having done C3/4 by my school
Posted from TSR Mobile

It would be worth studying modulus functions first, mainly how to draw them. It just takes any values - if the value is positive then the same value is returned. If it is negative then the negative of it is returned. Eg |10| = 10 and |-4| = 4, so if you're sketching a graph then reflect regions where y values are negative in the x axis.

Look at Zacken's post for starting off with x/x+2. These kind of fractions are as weird as it gets - otherwise the graphs shouldn't be too hard to sketch.

I often take points with nice x/y values eg x= 1, y= 1/3 x=4, y= 2/3 and get an idea of the shape like that (you'll remember the shapes of graphs from practice in time) and find vertical and horizontal asymptotes, test values to see the behaviour around the asymptotes.

Eg as x gets very large (test with calculator for x=10000 or whatever) x/(x+2) gets closer and closer to 1 but will never actually reach it. Apply similar logic to very negative values of x, or write y as (x+2-2)/(x+2), equivalent to 1 - (2/x+2)

Reply 6

davros

16

Original post by SeanFM

write y as (x+2-2)/(x+2), equivalent to 1 - (2/x+2)

This is probably going to be the most helpful advice when trying to plot a function such as this.

Use www.desmos.com/calculator to experiment with the functions and easily check your answers for any asymptotes or modulus functions. It's what I did and came in really useful in getting comfortable with them. :smile:

Reply 8

metrize

18

Original post by iMacJack

Gunna sound stupid but I'd rather know and sound stupid than not know and agree just to seem like I get it...

How do I go about drawing x/x+2?

If it's any consolation I've just been thrown into FP2 without having done C3/4 by my school
Posted from TSR Mobile

See what happens when the graph tends to positive and negative infinity, see how you would "break" the function, in this case when x=-2 as you cannot divide by 0 (its undefined)

Therefore you know the asymptote is at x=-2, and the graph tends toward y=1

FP2 inequalities question

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