how do you solve for the x and y intercepts of y=(3x)/(x^2+9)

Question

anonymous · Answer

To solve for the y intercept, set x=0 and solve:
$$y=(3)(0) / (0^2 + 9) = 0/9=0$$ So the y intercept is at 0,0. This is the origin. Since the origin is on both axes, 0,0 is also the x intercept. If this wasn't the case, you could also set y=0 and solve.

anonymous · Answer

ok, so anytime either x or y is plotted at (0,0) you dont even have to bother solving for the other point because you automatically know it is 0 right? and one more thing can you show me how you would solve to get x. I know it will be zero but i dont know how to get there from 3x/x^2+9=0

anonymous · Answer

Yes, if the origin is on the line, then it is both the y and x intercept. This is assuming however it only has one x intercept. A function can have more than one.

Set y=0 and solve:
$$0=(3x)/(x^2 + 9)$$ Multiply both sides by x^2+9
$$0=3x$$ Divide by 3:
$$0=x$$

anonymous · Answer

ah, i see. thanks, you've been very helpful

anonymous · Answer

You're welcome, glad I could help.

anonymous · Answer

hey man can i ask you another question?