Comments on: Graphs – Sketch & Win! http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: fggffggf http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9893 fggffggf Tue, 24 Jun 2008 05:15:52 +0000 http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9893 Actually it was a typo, the problem with lighting typing. Oh, and from this post on, I will identify myself as Li-sa and you might see my Li-sa footprints on some other blogs, like on squareCircleZ. The blog I originally had will be shut down soon so no website link is given here. Miss Loi, you don't have to creep in silently. Utmost silence looms like a thief. Actually it was a typo, the problem with lighting typing.
Oh, and from this post on, I will identify myself as Li-sa and you might see my Li-sa footprints on some other blogs, like on squareCircleZ.
The blog I originally had will be shut down soon so no website link is given here.
Miss Loi, you don't have to creep in silently. Utmost silence looms like a thief.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9880 Miss Loi Mon, 23 Jun 2008 17:49:30 +0000 http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9880 *Creeps in silently to add some diagrams and explanations to <b>fggffggf</b>'s answer to improve clarity* *Creeps in silently to add some diagrams and explanations to fggffggf's answer to improve clarity*

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9728 fggffggf Wed, 18 Jun 2008 07:00:39 +0000 http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9728 oh dear. Line 3: [pmath]x right 0[/pmath] from the negative x-axis: [pmath]y right -infty[/pmath] (I wonder why T must be placed next to Y.) <span class="highlight">Corrected for you ;) Fatty fingers?</span> oh dear. Line 3: x right 0 from the negative x-axis: y right -infty
(I wonder why T must be placed next to Y.)

Corrected for you ;) Fatty fingers?

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9727 fggffggf Wed, 18 Jun 2008 06:58:27 +0000 http://www.exampaper.com.sg/questions/e-maths/graphs-sketch-win#comment-9727 1. A possible value of n is -2. <div class="highlight"> Yes the sketch depicts a classic <m>y = a/x^2</m> graph which is one of the <strong>12 Graphs of Functions</strong> in your text book, where <var>a</var> > 0 In this case, <var>a</var> = 1 and <var>n</var> = -2. Actually to probe further, the graph looks similar for <var>n</var> = -2, -4, -6, ... (all negative even numbers) ;) </div> 2i. <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2008/06/graphs-sketch-answer-1.gif" alt="Answer Diagram" /> [pmath]x right 0[/pmath] from the positive x-axis: [pmath]y right +infty[/pmath] [pmath]x right 0[/pmath] from the negative x-axis: [pmath]y right -infty[/pmath] [pmath]x right +infty[/pmath]: [pmath]y right 1[/pmath] [pmath]x right -infty[/pmath]: [pmath]y right 1[/pmath] The curve on LHS of x-axis cuts x-axis at (-1,0). The curve has no maximum or minimum value. <b>and the curve passes through the given point!</b> <div class="highlight"> You did a great job in highlighting the <em>asymptotes</em> i.e. where the graph approaches zero or infinity. However EMaths students simply need to first recall the shape of <m>y = 1/x</m> (shown in grey in the diagram above), and then understand that the constant (+1) in <m>y = 1/x + 1</m> means that we're <strong>shifting upwards</strong> <m>y = 1/x</m> by one unit (see diagram above again). Lastly, substitute the values (1, 2) into the equation ⇒ 2 = 1/1 + 1 (LHS = RHS!) ⇒ the graph passes through this point! P.S. Don't assume that the graph will always pass through that dot in your question! Sometimes the graph passes to it's left/right/top/bottom - always sub in its coordinates to check! </div> 2ii. <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2008/06/graphs-sketch-answer-2.gif" alt="Answer Diagram" /> never cuts x-axis but as [pmath]x right -infty[/pmath], [pmath]y right 0[/pmath]. the curve passes through (0,1). The curve has no maximum or minimum value. <b>and the curve passes through the given point!</b> <div class="highlight"> Once again, EMaths students will recall the shape of the graph of <m>y = a^x</m> (they all intercept the <var>y</var>-axis at <var>y</var>=1 since <var>a</var><sup>0</sup> is always 1 and look similar in shape regardless of the value of <var>a</var>, as long as <var>a</var> is positive. So the only thing left to do is to substitute the values (1, 2) into the equation ⇒ 2 = 2<sup>1</sup> (LHS = RHS!) ⇒ the graph passes through this point! </div> Poor candidate in your picture. He has written something meaningful, not just freaking with abc's. <span class="highlight">Miss Loi too thinks that he deserves some sympathy marks for his back-to-basics description - to highlight the little things in life that we tend to take for granted ;)</span> 1. A possible value of n is -2.

Yes the sketch depicts a classic y = a/x^2 graph which is one of the 12 Graphs of Functions in your text book, where a > 0

In this case, a = 1 and n = -2. Actually to probe further, the graph looks similar for n = -2, -4, -6, ... (all negative even numbers) ;)

2i.

Answer Diagram

x right 0 from the positive x-axis: y right +infty
x right 0 from the negative x-axis: y right -infty
x right +infty: y right 1
x right -infty: y right 1
The curve on LHS of x-axis cuts x-axis at (-1,0).
The curve has no maximum or minimum value.
and the curve passes through the given point!

You did a great job in highlighting the asymptotes i.e. where the graph approaches zero or infinity.

However EMaths students simply need to first recall the shape of y = 1/x (shown in grey in the diagram above), and then understand that the constant (+1) in y = 1/x + 1 means that we're shifting upwards y = 1/x by one unit (see diagram above again).

Lastly, substitute the values (1, 2) into the equation ⇒ 2 = 1/1 + 1 (LHS = RHS!) ⇒ the graph passes through this point!

P.S. Don't assume that the graph will always pass through that dot in your question! Sometimes the graph passes to it's left/right/top/bottom - always sub in its coordinates to check!

2ii.

Answer Diagram

never cuts x-axis but as x right -infty, y right 0.
the curve passes through (0,1).
The curve has no maximum or minimum value.
and the curve passes through the given point!

Once again, EMaths students will recall the shape of the graph of y = a^x (they all intercept the y-axis at y=1 since a0 is always 1 and look similar in shape regardless of the value of a, as long as a is positive.

So the only thing left to do is to substitute the values (1, 2) into the equation ⇒ 2 = 21 (LHS = RHS!) ⇒ the graph passes through this point!

Poor candidate in your picture. He has written something meaningful, not just freaking with abc's.

Miss Loi too thinks that he deserves some sympathy marks for his back-to-basics description - to highlight the little things in life that we tend to take for granted ;)

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