Sketch Curves: y=5x^(3/4), y=-2x^(-3/2)

[Harmony]

Homework Statement

Sketch the curves with the following equations:
a) y=5x^(3/4)
b) y=-2x^(-3/2)

Homework Equations

The general equation of curves (circles, parabola, ellipse, hyperbola)

The Attempt at a Solution

It seems to me that this question is not exactly a coordinate geometry question. At first, I thought this is a parametric equation, but parametric equation use t instead of y. Then, I thought of substituting x with some other things. But that fails as well. (The fraction power make it not rational to be substituted by x^2, x^3 and so on.) The equation doesn't resemble general equation circles, parabola, ellipse, or hyperbola.

How should I attempt this question? Is equation of curves really useful to solve this question?

 

[radou]

You are given two functions y(x). Start with finding their domains.

 

[carbz]

There are other basic graphs of functions, so these would be some of them. Perahps it would be easier for you to re-write the fractional exponents. Well, that would be if you have gotten to that (or know how to).

I will let you know though, both of those equations don't resemble a circle, parabola, ellipse, or hyperbola.

As I said, try manipulating the exponents.

 

[HallsofIvy]

As pointed out, these are not quadratic functions and so their graphs are not conic-sections (circle, ellipse, hyperbola, parabola). Basically, just calculate y for a number of x values and draw a smooth curve through the points. As radou said, you'd better check the domains.