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Graphing tips needed

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pikachu975:
Hi, I was just wondering if anyone had tips or strategies for graphing questions? In my half yearly I was skipping a few questions to come back to at the end and I also left a graphing section until the end (15 marks) and it ended up taking me 40 mins - 1 hour so I didn't do the other questions I skipped. I can't seem to do graphing questions quickly so I just need to know how to be faster at them in general, thanks! E.g. we had to find domain etc of and graph cos^-1 (e^x) or something and it took me so long just to find domain/range and still got it wrong.

RuiAce:



When sketching curves that aren't given to you visually, but you know that it's composed of elementary functions, you shouldn't bother picturing too much if you can't. Instead, make a sketch of \(y=\cos^{-1}x\) and \(y=e^x\) explicitly. These sketches can be rough and small, but you need them to visualise what's going on.

We know that we're composing by taking cos-inverse OF the exponential. Therefore, the y-values of y=e^x should be compared to the x-values of y=arccos(x). This is an alternate way to deduce the domain.

I would not have been able to deduce the range without graphing it. To graph it, well fortunately because \(y=e^x\) and \(y=\cos^{-1}x\) are monotone we don't have to worry about stationary points or what not. So it helps to figure out the extremities.

Because our curve has domain \( x\le 0\) I would have analysed what happens at \(x=0\), and as \(x \to -\infty\). The latter makes the horizontal asymptote more obvious.



Graphing techniques vary for different questions. This was an example of function composition. If it were say, product, the techniques would be different.

armtistic:

--- Quote from: pikachu975 on April 27, 2017, 08:25:03 pm ---Hi, I was just wondering if anyone had tips or strategies for graphing questions? In my half yearly I was skipping a few questions to come back to at the end and I also left a graphing section until the end (15 marks) and it ended up taking me 40 mins - 1 hour so I didn't do the other questions I skipped. I can't seem to do graphing questions quickly so I just need to know how to be faster at them in general, thanks! E.g. we had to find domain etc of and graph cos^-1 (e^x) or something and it took me so long just to find domain/range and still got it wrong.

--- End quote ---

I would suggest maybe looking in to Terry Lee's textbook and also familiarising yourself with the changes that occur when you enact a certain change to a function for e.g. given y=f(x) you should know that y= |f(x)| will require you to flip everything below the x-axis up, and that y = f(|x|) requires you to mirror the curve from x>0 about the y-axis and etc.

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