Anyone got any tricky graph sketching questions?

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amoled
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As the title says does anyone have any difficult graph sketching problems or links?
I can't find many on internet. OK i havent covered hyperbolics but step standard or interview question style would be great.
Thanks for your help
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nuodai
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y^3=x^3+1
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amoled
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(Original post by nuodai)
y^3=x^3+1
oh k thanks ive drawn it
Is is similar to a y=x^3 graph but translated up 1 so it goes through (0,1) and then goes off to positive and negative infinity and has a point of inflection at the y intercept?
Thanks again

oh and gradient is infinite at 1,0.
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Farhan.Hanif93
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(Original post by amoled)
oh k thanks ive drawn it
Is is similar to a y=x^3 graph but translated up 1 so it goes through (0,1) and then goes off to positive and negative infinity and has a point of inflection at the y intercept?
Thanks again

oh and gradient is infinite at 1,0.
Nope. It has all those features although it doesn't look a whole lot like y=x^3 at all and the gradient is not infinite at (1,0). It has an oblique asymptote.
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abscef123
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How do you know it has an oblique asymptote? it's not a rational function so where did the oblique asymptote come from?
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RDKGames
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(Original post by abscef123)
How do you know it has an oblique asymptote? it's not a rational function so where did the oblique asymptote come from?
y = \sqrt[3]{x^3 - 1} which for very large x behaves close to y = \sqrt[3]{x^3} = x ... which is the oblique asymptote.

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