A vertical asymptote is a vertical line that a graph approaches but never touches. It occurs when the function approaches infinity or negative infinity as x approaches a certain value.
Imagine you are on a roller coaster ride and there is a point where the track suddenly shoots up into the sky, but you can't actually reach it. That point where the track shoots up represents the vertical asymptote.
Horizontal asymptote: A horizontal line that a graph approaches as x approaches positive or negative infinity.
Limit: The value that a function approaches as x gets arbitrarily close to a particular value.
Rational function: A function that can be expressed as the quotient of two polynomials.
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