Mathematical Methods - Pre-Exam 1 Advice for 2012

[Hutchoo]

Paul, do you think there will be any "sketch y = tan(...)/y = cos (...) " (trig graphs/exponentials/logs) graphs? I have hardly seen them pop up on the VCAA papers and I have a feeling one might be on this years!

[charmanderp]

Paul, do you think there will be any "sketch y = tan(...)/y = cos (...) " (trig graphs/exponentials/logs) graphs? I have hardly seen them pop up on the VCAA papers and I have a feeling one might be on this years!

If we have to draw a trig graph with a horizontal translation I will flip a table.

[Lasercookie]

If we have to draw a trig graph with a horizontal translation I will flip a table.

What's wrong with horizontal translations?

[charmanderp]

If we have to draw a trig graph with a horizontal translation I will flip a table.

What's wrong with horizontal translations?

They're not so bad but I just find them to be a bit tedious They mess around with the endpoints which means that they end up looking different on either side, etc. If you struggle to comprehend things physically like me then it's a bit of a bother.

[Hutchoo]

xD. You can always ROTE learn them. (lolthat'swhatvcemathsis)

[Truck]

If we have to draw a trig graph with a horizontal translation I will flip a table.

What's wrong with horizontal translations?

They're not so bad but I just find them to be a bit tedious They mess around with the endpoints which means that they end up looking different on either side, etc. If you struggle to comprehend things physically like me then it's a bit of a bother.

Pro sketching tip: Let's say the graph is 3sin(2x-pi/4) + 2 or 3cos(2x-pi/4) + 2, for a cos graph you make your starting point at (pi/8,5) and for a sin graph the starting point would be (pi/8, 2)... then if you know the Period which is 2pi/2 = pi, you can simply add/subtract the period within your given domain. ... so for a cos graph the next maximum t.p. would be at (pi/8 + pi, 5) and for a sin graph the next point where y=2 would be (pi/8+pi, 2). Now if you divide the period by 4, you get pi/4 - So with your knowledge of the general sin/cos graph, you'll know the exact value of each intercept/turning point simply by adding (in this case) pi/4 values and utilizing the translation/amplitude values.

[Lasercookie]

Pro sketching tip: Let's say the graph is 3sin(2x-pi/4) + 2 or 3cos(2x-pi/4) + 2, for a cos graph you make your starting point at (pi/4, 5) and for a sin graph the starting point would be (pi/4, 2)...

You forgot to take into account the 2x there, so those coordinates are off. For the cos it should be (pi/8,5) and for the sin it should be (pi/8,2)

[Truck]

Pro sketching tip: Let's say the graph is 3sin(2x-pi/4) + 2 or 3cos(2x-pi/4) + 2, for a cos graph you make your starting point at (pi/4, 5) and for a sin graph the starting point would be (pi/4, 2)...

You forgot to take into account the 2x there, so those coordinates are off. For the cos it should be (pi/8,5) and for the sin it should be (pi/8,2)

yeah you're right, lol how embarrassing. thanks laseredd!

[HERculina]

Horizontal and vertical translations + dilations from both axis + reflection for circular function graphs = death of me.

[Shenz0r]

Draw out sketches for each of the transformations in order. It will give you a good idea of what the important points (intercepts, endpoints, stationary points) will be.

[paulsterio]

For horizontally translated trig graphs, just think of it as moving the axes rather than moving the graph, it makes life so much easier

Alternatively, just find all intercepts and turning points and join the dots

Anyways, here's Exam 2 - enjoy - Mathematical Methods - Pre-Exam 2 Advice for 2012

[ilovestudying]

Last question: what is the domain of composite function? Is it the same with the domain of the inner function? Thanks!

[BubbleWrapMan]

Yes it's the domain of the inner function after the range has been restricted

[soccerboi]

For f(g(x)) to exist, the range of g(x) must be a subset of the domain of f(x) right?

[Hancock]

Correct