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Determine the vertical asymptote(s) if one exists.$$f(x)=\frac{x-2}{x^{2}-4}$$

$$x=-2$$

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

Oregon State University

McMaster University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Determine the vertical asy…

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Find the vertical asymptot…

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Determine all horizontal a…

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Determine the horizontal a…

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Find all vertical asymptot…

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Find the equation of any h…

what X approaches The number eight function venue becomes infinite. Then the nine x echoes is a vertical has marked How could this situation happened for rational function? Assumption condition is that the denominator is zero at this point A and the numerator event. In this way, the X approaches a the denominator approaches zero and the numerator approaches some counsel number and consequently the whole function becomes a very large positive or negative number. Hence, the criterion to find Vertical s motto is that the denominator vanishes and the numerator does not. For this exercise, we can first factor the denominator into two parts. And then it's easy for us to say that the X equals minus two x equals to the denominator is zero, but notice that X equals two. The numerator is also zero. And if you know how to calculate the limit when X equals two, you will see that the limit is 1/4 and therefore X equals two is not a vertical as model, but when X equals miners to the numerator is minus four and therefore the only vertical as model for this function is X equals minus two

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