Question 152178
Let's start with finding the y-intercept. When x is equal to 0, we know that the graph is crossing the y-axis. So, when we have x be 0 in the equation:
{{{y = 3x/(x^2 + 1)}}}
{{{y = 3(0)/(0^2 + 1)}}}
{{{y = 0/1}}}
{{{y = 0}}}
It looks like the y-intercept is at y = 0.
<br>Now let's find the x-intercept. When y is equal to 0, we know that the graph is crossing the x-axis. So, when we have y be 0 in the equation:
{{{y = 3x/(x^2 + 1)}}}
{{{0 = 3x/(x^2 + 1)}}}
{{{0*(x^2 + 1) = (x^2 + 1)*(3x/(x^2 + 1)) }}}
{{{0 = 3x}}}
{{{x = 0}}}
It looks like the x-intercept is at x = 0.
<br>Now let's look for the asymptotes. An asymptote happens when the value of y is undefined. The easiest way to find an asymptote is for the bottom of the fraction to equal 0. In this case:
{{{y = 3x/(x^2+1)}}}
{{{x^2 + 1 = 0}}}
{{{x^2 = -1}}}
Because the answer to this isn't a real number, there are no asymptotes.