Help with graph transformations

3

Graphs have always been a weak point for me as I struggle with both visualizing and drawing them, however as i get closer to the actual exams (a level) It's becoming harder to just accept as a weakness. I've spent a lot of time revising them (especially the transformations) but they still just never make sense to me. Every time i think i have got them down i realise i haven't. If anyone has got any tips on how to get better at drawing/visualizing graphs generally as well as specifics for the transformation questions and also the weird trig graphs i.e sec or arccos please let me know. It feels very annoying to drop marks on these relatively easy questions especially because if its like question 4 and i know i have it wrong it stays in my head for the rest of the paper and i do bad on the bits im good at.

Reply 1

mqb2766

21

Original post

by C0gg

Graphs have always been a weak point for me as I struggle with both visualizing and drawing them, however as i get closer to the actual exams (a level) It's becoming harder to just accept as a weakness. I've spent a lot of time revising them (especially the transformations) but they still just never make sense to me. Every time i think i have got them down i realise i haven't. If anyone has got any tips on how to get better at drawing/visualizing graphs generally as well as specifics for the transformation questions and also the weird trig graphs i.e sec or arccos please let me know. It feels very annoying to drop marks on these relatively easy questions especially because if its like question 4 and i know i have it wrong it stays in my head for the rest of the paper and i do bad on the bits im good at.

Can you post an example or two. Sketching trig curves shouldnt be too bad by just plotting a few points on the curve (so the gcse 0,30,45,60,90 ....) and the arctrig stuff can be derived by reflecting in the line y=x for the appropriate domain.

(edited 9 months ago)

Reply 2

C0gg

OP

3

an example or 2 of questions i struggle with or what my drawings look like?

Reply 3

mqb2766

21

Original post

by C0gg

an example or 2 of questions i struggle with or what my drawings look like?

Both would be helpful but the questions would be the main thing.

Reply 4

C0gg

OP

3

this is the question that made me ask online, but its literally just any math's that involves drawing a graph/ visualizing how a graph looks

Reply 5

C0gg

OP

3

also something like this i find the actual algebra very easy but the minute i have to draw them it gets much harder

Reply 6

mqb2766

21

Original post

by C0gg

this is the question that made me ask online, but its literally just any math's that involves drawing a graph/ visualizing how a graph looks

For the last part, practice will improve things and theres no silver bullet but
y = 1/x
should be one you know, but rewriting it as
yx = 1
means if x is large, y is smalll (product is 1) and vice versa. Similarly (1,1) obviously lies on the curve. When x is negative, so is y (quadrant 3), so thats enough really to get the two curve parts with a vertical asymptote at x=0 and a horizontal asymptote at y=0 (as there is no solution to 0x=1 or 0y=1).

sec(2x) = 1/cos(2x) and the basic cos is easy enough to sketch. cos(2x) means that when x=pi, the point is cos(2pi) so it osciallates twice as fast as the normal cos curve. 1/cos(2x) must then be <= -1 or >=1 as its the reciprocal of cos(2x) and it will have vertical asymptotes when cos(2x)=0 so x=pi/4,3pi/4, ..

See if you can get that one right / you understand and post any problems.

Reply 7

mqb2766

21

Original post

by C0gg

also something like this i find the actual algebra very easy but the minute i have to draw them it gets much harder

For aii) you should be able to sketch a quadratic, 4x^2 has a min at (0,0) and is the usual "u" shape ... With quadratics, completing the square usually helps sketching them but it should be trivial for this one.

bii) pretty much as above, complete the square for fh(x) and sketch that. Completing the square has the vertical and horizontal shifts explicit and the scaling applied to the quadartic.

12) is again completing the square, what do you think about it, even if thats wrong?

Help with graph transformations

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