Drawing Graphs

hey, i was wondering if anyone could help me with drawing graphs. i havent got a graphic calculator and have my FP1 exam in june. for this i may have to draw graphs to solve inequalities etc etc...

im fine with simple graphs, however when it comes to things like: y = x - 2/(2x +5) that i dont know what to do!

i know the shape of a graph with a fraction like this has asymptopes (sp?) but i dont know where to plot the points.

any advice would be appreciated! thanks.

Reply 1

meef cheese

You only need to sketch them so don't worry about being too accurate. If I had a function like that, I would put it all over a common denominator.

Then, points to consider are:

x=0
y=0
when does top line = 0, f(x) = 0
when does bottom line = 0, f(x) = infinity
Consider the points just before and just after the bottom line equals zero. Is f(x) positive or negative? This tells you whether f(x) --> +ve or -ve infinity
Consider what happens when x--> +ve and -ve infinity

And you should be able to work out the gaps in between

Reply 2

Bengaltiger

\large y = x - \frac{2}{2x + 5}

Can be written as

\large y = \frac{2x^2 +5x - 2}{ 2x + 5}

You can find the assymptotes. Also you can find out where y is when x = 0. Also when x tends to the assymptotes, is it possitive or negative?

You can sketch the graph quite easily with this knowledge.

Reply 3

Christophicus

Another handy thing to do is to take the derivative of the function, so you can determine whether its gradient is positive or negative at a particular point.

Reply 4

Loz2402

thanks, i will do some practise questions before the exam and try and sketch the graphs.

also, another thing about the graphic calculator, does anyone have them? would you say they would be a wise investment for further modules? im going to go on and do A2 further maths and maths as well, and then most probably maths at uni. should i wait a while and get one later? cos its a lot of money! and once i get this sorted should be ok.

Reply 5

Morbo

graphic calculators are useful learning tools because they allow you to sketch functions quickly, which is useful if you want to know their behaviour as part of another problem. however, over time, this does have a negative effect on your graph-sketching skills which you might need in an exam!

a lot of them do calculus, matrix operations etc, and so they are also useful for checking your answers to these kinds of problems. however used incorrectly, they can make you a very lazy maths student! (i remember getting so annoyed with 3x3 inverses at A-level that I just typed my homework problems into the calculator...shocking...)

you're not allowed graphical calculators in exams, so it's dangerous to rely on them normally.

as for uni, a graphical calculator is not essential, at least for physics anyway. mathematicians probably have even less use for them. what is useful are programs like Maple or MathCad which have much more powerful functions than a graphical calculator, and they're easier to use!

Reply 6

Christophicus

Worzo

graphic calculators are useful learning tools because they allow you to sketch functions quickly, which is useful if you want to know their behaviour as part of another problem. however, over time, this does have a negative effect on your graph-sketching skills which you might need in an exam!

a lot of them do calculus, matrix operations etc, and so they are also useful for checking your answers to these kinds of problems. however used incorrectly, they can make you a very lazy maths student! (i remember getting so annoyed with 3x3 inverses at A-level that I just typed my homework problems into the calculator...shocking...)

you're not allowed graphical calculators in exams, so it's dangerous to rely on them normally.
as for uni, a graphical calculator is not essential, at least for physics anyway. mathematicians probably have even less use for them. what is useful are programs like Maple or MathCad which have much more powerful functions than a graphical calculator, and they're easier to use!