Curve Sketching Questions (1 Viewer)

[housemouse]

1) What does x^(1/3) look like?
2) How do you find the domain and range?
3) How would you sketch log and exponential graphs if you get something like y = e x^2 or y = log(x^2-1) to the base e?
4) How do you find the assumptotes of y = e -x^2?

 

[Mountain.Dew]

1) What does x^(1/3) look like?
2) How do you find the domain and range?
3) How would you sketch log and exponential graphs if you get something like y = e x^2 or y = log(x^2-1) to the base e?
4) How do you find the assumptotes of y = e -x^2?

1) x^(1/3) kinda looks like a tan^-1x function, with a point of inflexion at the origin. however, unlike the tan^-1x function, it has no domain or range restrictions.
2) domain: all real x range: all real y
3) for y=ex^2, its quite simply a normal y=x^2 graph, but all the y values are multiplied by e. its like y=4x^2 or y=6x^2. e is merely a constant.

for y=log(x^2-1) ==> simply graph y=x^2-1 THEN take the LOG (base e) of the y-values of the graph you've drawn.

4) y= -ex^2...there is no assymptotes.

 

[Templar]

The assymptote of y=Exp[-x^2] would be y=0. It's the value y approaches as x approaches +/- infinity.