How many vertical asymptotes can a function have?
A function can have zero, one, or multiple vertical asymptotes
A function can have zero, one, or multiple vertical asymptotes.
Zero vertical asymptotes: If a function does not have any vertical asymptotes, it means that the graph of the function does not approach any vertical line as x approaches a certain value. In other words, the function does not exhibit any unbounded behavior in the vertical direction.
One vertical asymptote: A function may have one vertical asymptote, typically denoted by a vertical line of the form x = c. This occurs when the function approaches positive or negative infinity as x approaches a specific value. The graph of the function approaches the vertical line without ever intersecting it.
Multiple vertical asymptotes: A function can also have more than one vertical asymptote. This happens when the graph approaches different vertical lines as x approaches different values. Each vertical asymptote represents a distinct value for which the function exhibits unbounded behavior.
The number of vertical asymptotes a function can have depends on its behavior as x approaches different values. It is important to note that a function can have both horizontal asymptotes (as x approaches positive or negative infinity) and vertical asymptotes simultaneously. Additionally, the presence or absence of vertical asymptotes is determined by the properties of the function and its algebraic expression.
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