# FP1 Rational Functions Question

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If anyone could help with this FP1 question, I would be very grateful!

A curve has an equation y=(x^2+2)/(x^2-4x)

a)Write down the asymptotes (Done this part)

b)i) Prove no part of the graph exists in the region -1 <= y <= 1/2 (part i'm having trouble with)

ii) Find the co-ordinates of the turning point on (may become easier after I know how to do part i)

c) Sketch the curve (I can do this too)

Any help would be great thanks

A curve has an equation y=(x^2+2)/(x^2-4x)

a)Write down the asymptotes (Done this part)

b)i) Prove no part of the graph exists in the region -1 <= y <= 1/2 (part i'm having trouble with)

ii) Find the co-ordinates of the turning point on (may become easier after I know how to do part i)

c) Sketch the curve (I can do this too)

Any help would be great thanks

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#2

(Original post by

A curve has an equation y=(x^2+2)/(x^2-4x)

b)i) Prove no part of the graph exists in the region -1 <= y <= 1/2 (part i'm having trouble with)

**KieRigby**)A curve has an equation y=(x^2+2)/(x^2-4x)

b)i) Prove no part of the graph exists in the region -1 <= y <= 1/2 (part i'm having trouble with)

If yes, notice that horizontal lines have equation , for any given real value of . So you want to find the values of , where has

**no**solutions as this will give you the "horizontal lines" that do not meet the curve, which in turn tells you that the curve doesn't exists there.

Try rewriting as a quadratic equation and consider it's discriminant (recall that a quadratic equation has no solutions if the discriminant is negative).

ii) Find the co-ordinates of the turning point on (may become easier after I know how to do part i)

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Try rewriting as a quadratic equation and consider it's discriminant (recall that a quadratic equation has no solutions if the discriminant is negative).

I understand you're explanation, however the question asks prove no part of the graph exists in region -1 <= y <= 1/2. How can this be possible? The line cannot intersect with the curve and not intersect with it at all? Perhaps the question is wrong?

Either way, your explanation was perfect! Thank you

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#4

(Original post by

Thanks for your help

I understand you're explanation, however the question asks prove no part of the graph exists in region -1 <= y <= 1/2. How can this be possible? The line cannot intersect with the curve and not intersect with it at all? Perhaps the question is wrong?

**KieRigby**)Thanks for your help

I understand you're explanation, however the question asks prove no part of the graph exists in region -1 <= y <= 1/2. How can this be possible? The line cannot intersect with the curve and not intersect with it at all? Perhaps the question is wrong?

"No part of the graph existing in the region " is the same thing as saying "any horizontal line drawn (with ) will not intersect the curve". The natural thing to do next is to consider intersections of the curve with the arbitrary horizontal line y=c, and showing that has no solutions for the range . As explained above, this is done by considering the discriminant.

it would be a lot easier to explain with a picture, but it's late and I'm tired. There's nothing wrong with the question.

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(Original post by

Take another read of the explanation, it may help. Think of it this way:

"No part of the graph existing in the region " is the same thing as saying "any horizontal line drawn (with ) will not intersect the curve". The natural thing to do next is to consider intersections of the curve with the arbitrary horizontal line y=c, and showing that has no solutions for the range . As explained above, this is done by considering the discriminant.

it would be a lot easier to explain with a picture, but it's late and I'm tired. There's nothing wrong with the question.

**Farhan.Hanif93**)Take another read of the explanation, it may help. Think of it this way:

"No part of the graph existing in the region " is the same thing as saying "any horizontal line drawn (with ) will not intersect the curve". The natural thing to do next is to consider intersections of the curve with the arbitrary horizontal line y=c, and showing that has no solutions for the range . As explained above, this is done by considering the discriminant.

it would be a lot easier to explain with a picture, but it's late and I'm tired. There's nothing wrong with the question.

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#6

(Original post by

Funny story. The question was wrong, my teacher made a mistake when producing the work sheet. So there is something wrong with the question.

**KieRigby**)Funny story. The question was wrong, my teacher made a mistake when producing the work sheet. So there is something wrong with the question.

Is that the mistake you are referring to?

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(Original post by

The inequality -1 <= y <= 1/2 in the question should have been -1 < y < 1/2.

Is that the mistake you are referring to?

**notnek**)The inequality -1 <= y <= 1/2 in the question should have been -1 < y < 1/2.

Is that the mistake you are referring to?

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#8

What is a rational function... it is not on the FP1 edexcel syllabus. We only have complex numbers, iteration, parametric stuff, matrices, series and induction

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#9

(Original post by

What is a rational function... it is not on the FP1 edexcel syllabus. We only have complex numbers, iteration, parametric stuff, matrices, series and induction

**MathMeister**)What is a rational function... it is not on the FP1 edexcel syllabus. We only have complex numbers, iteration, parametric stuff, matrices, series and induction

It's nothing special - you may even study them without knowing what they're called

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#10

**MathMeister**)

What is a rational function... it is not on the FP1 edexcel syllabus. We only have complex numbers, iteration, parametric stuff, matrices, series and induction

It's not part of Edexcel, but for AQA FP1 you need to know about rational functions where p and q have degree 1 or 2 e.g. . They study things like asymptotes, maxima, minima, intersection points etc.

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#11

consider y(x^2-4x)=x^2+2

then use discriminant to find range of values of y hence solving it. Takes a few minutes.

Posted from TSR Mobile

then use discriminant to find range of values of y hence solving it. Takes a few minutes.

Posted from TSR Mobile

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(Original post by

consider y(x^2-4x)=x^2+2

then use discriminant to find range of values of y hence solving it. Takes a few minutes.

Posted from TSR Mobile

**physicsmaths**)consider y(x^2-4x)=x^2+2

then use discriminant to find range of values of y hence solving it. Takes a few minutes.

Posted from TSR Mobile

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#13

(Original post by

The question is incorrect though, it is unsolvable.

**KieRigby**)The question is incorrect though, it is unsolvable.

Posted from TSR Mobile

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