HSC Tips - Graphs (1 Viewer)

[McLake]

Here is the first in a series of "HSC Tips" threads. Please feel free to suggest more tips.

Tips for Graphs:
- Plot and LABEL axis (including the origin)
- Plot critical points (end points, turning points, x/y intercepts, etc)
- Plot asymtopes
- Check behaviour of graph in the different regions created by the critical points before drawing
- Look at behaviour as x -> +/- "infinity"
- Draw LARGE graphs, at least 1/2 page of exam booklet.
- DO NOT use calculas to determine aspects of the graph.

- Know the shape of "standard" graphs:
-- y = 1/f(x)
-- y = |f(x)|
-- y^2 = f(x) [Treat this as y = +/- sqrt(f(x))]
-- y = f^-1(x) [Reflected through y=x]

 

[Affinity]

Q: Do we have to show how we determine the properties of the curve?

A: No. There is no need to show why you have draw a curve the way you have.

 

[Affinity]

Q: How about addition/division/multiplication/etc of 2 graphs? do we need to find the Points of inflexion, Maxima and Minima?

A: Yes (sorry, this changes some of the points I have made so far, but I think it is clear where it is appropriate to use calculas)

 

[Rahul]

Q:Do we need to show how we found the POI, Maxima and Minima? [i generally ffind the shape of the graph, but miss out showing the inflection point, what should i look for? do i need to find the second derivative?

 

[McLake]

Originally posted by Rahul
Q:Do we need to show how we found the POI, Maxima and Minima? [i generally ffind the shape of the graph, but miss out showing the inflection point, what should i look for? do i need to find the second derivative?

A: Yes
Show possible inflection by checkning concavity with second derivitive, prove inflection with first derivitive ....

 

[Rahul]

Q: critical points:
1. vertical tangent- gradient is +- (infinity) at a vertical tangent
2. angular point- gradient changes on each side of an angular point

are they correct? in arnolds book, it is stated that there are 4 different types of critical points, what are they?

 

[loser]

Originally posted by McLake
Show possible inflection by checkning concavity with second derivitive, prove inflection with first derivitive ....

first derivative?

 

[Rahul]

y'....f'(x)?

when you first differentiate a function

 

[loser]

So how do you prove an inflexion with the first derivative?

I thought you only needed to check either side of the second derivative where f''(x)=0?

I can't believe I don't know this

 

[redslert]

it's one mark if you don't check!
one mark is a lot!!!!

could be 2 marks if there was 2 HIP!

 

[ricenoodles]

Originally posted by Rahul
y'....f'(x)?

when you first differentiate a function

what do we need to do to work out how to draw these types of graphs and the same for integration of f(x)?

 

[McLake]

Originally posted by loser
So how do you prove an inflexion with the first derivative?

I thought you only needed to check either side of the second derivative where f''(x)=0?

I can't believe I don't know this

Check concavity pattern, should be /-/ or \-\

 

[Rahul]

isnt that the nature of stationary points mclake?
it can work in the same manner for concavity too...

Originally posted by ricenoodles
what do we need to do to work out how to draw these types of graphs and the same for integration of f(x)?

i'm not sure what you mean, sorry? rephrase

 

[ricenoodles]

Originally posted by Rahul
i'm not sure what you mean, sorry? rephrase

for example, they give u a sketched graph [f(x)] and they ask you to sketch #f(x).
where # = integration sign

 

[Rahul]

oh ok. you mean they have given you y' and you have to graph y.

well the zero's of y' = stationary points on y.
secondly you would look at where the y', the gradient of y is +ve or -ve. this will show where y is increasing ( / ) or decreasing ( \ ).

thats all the info you can use from the y' graph. unless i missed something out.

 

[McLake]

Originally posted by Rahul
oh ok. you mean they have given you y' and you have to graph y.

well the zero's of y' = stationary points on y.
secondly you would look at where the y', the gradient of y is +ve or -ve. this will show where y is increasing ( / ) or decreasing ( \ ).

thats all the info you can use from the y' graph. unless i missed something out.

Also check what happens as x -> +/- infinity.
And check what happens near asymtopes on y' (which will genrally become asymtopes or paraboilc curves on y)

 

[maple_leaf_matt]

transformations

does anyone know how to do transformations from f(x) to eg>

|f(x)|,
f(|x|),
|f(|x|)|,
f-1(x) (inverse)
fSQRT(x)
??

or the trig ones!!!
cos f(x), sin etc!
Thanks i need help!!!!

 

[Constip8edSkunk]

|f(x)|, stuff below the x axis gets reflected above
f(|x|), the x>0 part of the graph reflected across the y axis
|f(|x|)|, combine the above
f-1(x) (inverse) reflect across y=x
fSQRT(x) above y=1 : plot below f(x); below y=1: plot above f(x)... hav a look at the text books

 

[enak]

Thanks, I was wondering wtf |f(|x|)| was :S

 

[maple_leaf_matt]

so its 11.50 on the night b4 my 4u
i wish everyone the best of luck in this challenging exam! lets also be confident in the knowledge that we are going to get scaled like a motherfcuker! haha, love u all
MLM