drawing sqrt(f(x)) (1 Viewer)

[.ben]

When drawing graphs with sqrt(f(x)), how do you know when the branch has an inflexion point or not, without differentiating?

thanks

 

[insert-username]

My understanding of the square root of the f(x) is that it looks like the original function except it's flatter and doesn't exist when f(x) < 0. If the original function has an inflexion point, the square root of it will too at the same point (but flatter and lower down on the y-axis).


I_F

 

[.ben]

oh ok, but sometimes you get graphs which don't have inflections but after taking sqrt you get an inflection. i just need to know what kind of shape it is. e.g. does it branch off like a parabola or cubic etc. i drew a diagram, it's just the shape of the red branch.

thanks again

 

[Raginsheep]

From what I remember, its actually fairly hard to determine the square root of certain graphs without resorting to calculus.

 

[adgala]

your picture looks correct as long as where the 2 graphs intersect is where f(x) = 1 and sqrt f(x) = 1

 

[_ShiFTy_]

Just ignore the "dont use calculus part"...as long as you cross out the calculus stuff off on your hsc paper, the markers arent supposed to read it

 

[.ben]

I drew another one can someone tell me which one it is?

 

[_ShiFTy_]

The bottom part of the graphs dont exist...

 

[Riviet]

From Shifty's point, remove the red bits below the x-axis and it should be right.

 

[.ben]

ok i drew two graphs, which on eis correct?

 

[ianc]

You have drawn ±sqrt[f(x)]; so if you remove all the parts below the x axis youll be fine because the question only required you to draw +sqrt[f(x)]

Hope this helps!

 

[Riviet]

Here's a neater diagram.

 

[housemouse]

You could draw the lines a bit flatter

 

[Riviet]

I didn't want to make the intersection points with y=1 look like inflection points, that's why the black and red lines are a little too close, but you get the idea. :uhhuh:

 

[.ben]

wait, so are there inflections of teh sqrt(f(x)) or not?

 

[shsshs]

no note really. especially when ur just given the sketch of a function f(x) and not told the actual function.

if you are given a function, dont draw inflexions initially but you should check if you have time

 

[Raginsheep]

Normally, if they specifiy "without using calculus", then they don't expect you to know where the inflections if they even exist.

Or you could just look at the marking scheme. 2marks generally means correct shape and stat points.