ATAR Notes: Forum
HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: e2503 on September 15, 2019, 03:48:30 pm
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Hi everyone, :)
I`m a bit confused about graphing reciprocal functions, if someone could send help it would be very much appreciated ;D.
I was taught that when graphing reciprocal functions, i should first graph the original function in the denominator and work from then onwards. When graphing the original function do i have to graph the product of the denominator function and the numerator or just graph the denominator function? For instance, for y= -3x/ (x^2-16) do i graph -3x(x+4)(x-4) first or graph just (x+4)(x-4) as the original function?
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I'm assuming this is for the new Year 11 syllabus?
If so, using the word "denominator function" is perhaps the cause of ambiguity here. The idea is that you should start with the sketch of \( (x+4)(x-4)\), and then use that curve to sketch \( \frac{1}{(x+4)(x-4)} \).
Then, you apply the multiplication technique on \(-3x\) and \( \frac{1}{(x+4)(x-4)}\).
(So in step 1, the original function is indeed \((x+4)(x-4)\). But in the second step, because we're doing a multiplication, there's technically speaking two "original" functions.)
Not sure how \(-3x(x+4)(x-4)\) would be useful here, unless it's just a misinterpretation, or a typo.