anonymous 5 years ago for which of these equations is y a function of x? y=3x^3 xy=1 y^2=x y^3=8x

1. anonymous

I'm not really sure how to answer this. Any of these y could be a function of x except the x = y^2 one because there's 2 possible outputs for the same input.

2. anonymous

k thanks

3. anonymous

Y is a function of x if for e given x there is only one corresponding y. y=3x^3 is OK xy=1 => y=1/x is OK y^2=x => $y = \sqrt{x}$ is OK y^3=8x =>$y = \sqrt[3]{8x}$ is OK You can graph these functions and when you draw a vertical line from any x value the line should intersect the graph in only one point. (only one y value for each x)

4. anonymous

$$y^2 = x \implies y = \pm \sqrt{x}$$ Therefore it is not a function because for any one value for x, you have 2 possible values for y.

5. anonymous

My mistake it is a function for x$X \ge 0$

6. anonymous

Ok one more try it is a function if the function range is $Y \ge 0$