I'm trying to understand why some quadratic functions have 2 vertical asymptotes
f(x) = x^2 + 2x, having x = 0 and x = -2
Hi there.
Quadratic functions do not have asymptotic behavior. Also, Quadratic functions are not Rational functions.
In your example, the vertical lines described by x = 0 and x = -2 are not asymptotes.
Please look up the definition of "asymptote" in your text, and post what you see here. We will help you interpret the definition correctly.
If you don't like your text, then google the subject for definitions and examples, and post what you find.
You may also google keywords
images vertical asymptotes, to study some images.
I always thought asymptotes were the point that the function could never cross
This is not correct. Asymptotes are not points; they are straight lines.
It's true that the graph of an asymptotic function will never touch or cross a
vertical asymptote, but such graphs can touch or cross horizontal or slant asymptotes at other locations in the domain where the function does not display asymptotic behavior.
With this function, the asymptotic behavior occurs when x is getting very large or very small. Note the horizontal dotted line (y=1); that line is a horizontal asymptote because the function's graph is getting closer and closer to that line,
as x heads toward positive infinity. Note that the function's graph crosses that line elsewhere.
As x heads toward negative infinity, this function also has asymptotic behavior. The function's outputs are getting closer and closer to the x-axis. Therefore, the line y=0 is also a horizontal asymptote. The function's graph crosses this asymptote, also, at the origin.
Cheers
