SOLUTION: Can you identify the intercepts and asymptotes of this equation? f(x) = (3x) / (x^2 + 1)

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Question 152178: Can you identify the intercepts and asymptotes of this equation?
f(x) = (3x) / (x^2 + 1)
Answer by mducky2(62) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F%28x%5E2+%2B+1%29
y+=+3%280%29%2F%280%5E2+%2B+1%29
y+=+0%2F1
y+=+0
It looks like the y-intercept is at y = 0.

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%2F%28x%5E2+%2B+1%29
0+=+3x%2F%28x%5E2+%2B+1%29
0%2A%28x%5E2+%2B+1%29+=+%28x%5E2+%2B+1%29%2A%283x%2F%28x%5E2+%2B+1%29%29+
0+=+3x
x+=+0
It looks like the x-intercept is at x = 0.

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%2F%28x%5E2%2B1%29
x%5E2+%2B+1+=+0
x%5E2+=+-1
Because the answer to this isn't a real number, there are no asymptotes.