Can someone show me how to sketch this curve? (1 Viewer)

[softchillisauce]

Hi everyone!
Graphs isn't exactly the hardest topic out there. I can handle everything but one question type.
Can someone tell me how to graph y=f(x^2)? D:

Thanks,
Softchillisauce

 

[braintic]

Hi everyone!
Graphs isn't exactly the hardest topic out there. I can handle everything but one question type.
Can someone tell me how to graph y=f(x^2)? D:

Thanks,
Softchillisauce

It is similar to sketching y=f(|x|).

For starters, it is even, and x^2 can't be -ve. So drop the LHS of the curve, and once you get the RHS, just reflect it across the y-axis.

Secondly, y'=2x.f'(x^2). So there will be a stationary point at x=0. So unlike y=f(|x|), you won't get a sharp point at x=0.

Finally [unlike y=f(|x|)], the curve becomes 'squashed' horizontally. Features that were previously at x=4 now occur at x=2, those that were previously at x=9 now occur at x=3, etc (however the part of the curve that was between x=0 and x=1 is 'stretched' Features at x=1/4 are now at x=1/2, etc.). The y-values of these features are unchanged.

 

[softchillisauce]

Thanks mate. It really helped me!