We haven't learnt how to design the graphic when the denominator has x, and it cannot be simplified. Can you just tell me the steps or lead me to a web address?
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looks like they explain a similar example here: https://www.youtube.com/watch?v=hWjMovgqvi4 – Surb Mar 04 '15 at 15:46
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1If you are only interested in the result and not the method you can go to http://www.wolframalpha.com/ – Marc Mar 04 '15 at 15:51
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Start by finding some points on the graph (you supply an $x$ value and compute $y$). – hardmath Mar 04 '15 at 15:51
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Please provide some additional context. Are you, for example, taking calculus? (If so, there are simple techniques for making a very accurate sketch.) – Barry Cipra Mar 04 '15 at 16:09
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No, no I just have to do it on my copybook, but we were never explained it. – seda Mar 04 '15 at 16:10
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3Do you know about asymptotes? Do you know how to find the roots of a quadratic? It's hard to give good guidance without knowing what techniques you are expected to use. The one piece of advice I can offer is to start by factoring a $3$ out of the denominator, and manipulate the equation into the form $$y=mx+b+{c\over2x+1}$$. – Barry Cipra Mar 04 '15 at 16:22
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if you know (a) long division, (2) quadratic equation, then it is not not hard to sketch this graph or any rational function where one of the numerator or the denominators is a quadratic. – abel Mar 04 '15 at 19:01
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Let $f(x)=\frac{2x^2+13x+9}{6x+3}$ and try to find the values of $f$ for different values of $x$, find these pairs on and x-y axis and you will have a picture of this function:
and more and more points:
of course comments above are very helpful.
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