f(x) = fraction {x}{square root {x^2 + 3} - 2x } find the verticle asymptotes of f(x) Find the...

Question:

{eq}\displaystyle f(x) = \frac {x}{\sqrt {x^2 + 3} - 2x } {/eq}

a) find the verticle asymptotes of {eq}f(x) {/eq}

b) Find the horizontal asymptotes of {eq}f(x), {/eq} make sure with both direction of the {eq}x-axis. {/eq}

Finding Asymptotes Of Functions

Functions can vertical, horizontal and slant asymptotes.

Vertical ones can appear in fractions, when the denominator is 0, in logarithmic functions at 0 and tan/cot functions, as they are fractions by their nature.

Horizontal asymptotes appear if the function's value approach to a particular number for {eq}x\to\pm\infty {/eq}.

Slant asymptotes appear when we have a fraction of polynomials and the maximal power of the numerator is 1 more than the one of the denominator.

Answer and Explanation:

The given function is a fraction, so it can have a vertical asymptote, if the denominator is 0 for some values of x. It can also have a horizontal...

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Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 9
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