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List all asymptotes (both horizontal and vertical) of the rational function: f(x) = \frac{10x -...

Question:

List all asymptotes (both horizontal and vertical) of the rational function:

{eq}f(x) = \displaystyle \frac{10x - 3}{8 - 7x} {/eq}

Rational Function:

The rational functions present two asymptotes that serve to limit the curves. These curves never intercept asymptotes. Asymptotes are straight lines that can have a vertical, horizontal and in exceptional cases inclined orientation.

Answer and Explanation:

Function:

{eq}f\left(x\right)=\frac{10x-3}{8-7x} {/eq}


Horizontal Asymptote:

The horizontal asymptote is given by the denominator of the fraction.

{eq}\begin{align*} 8-7x&=0 \\ 7x&=8 \\ x&=\frac{8}{7} \end{align*} {/eq}


Vertical Asymptote:

The vertical asymptotes when the denominator degree and the numerator degree are equal is given by the coefficient between the coefficients.

{eq}\begin{align*} y&=\frac{10}{-7} \\ y&=-\frac{10}{7} \end{align*} {/eq}


Learn more about this topic:

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Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
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