Characteristics of Rational Functions
Determine the Horizontal and Vertical Asymptote for each of the following functions. Write each Asymptote as an equation. If an Asymptote doesn't exist, write DNE\displaystyle {D}{N}{E}.
Rational FunctionHorizontal AsymptoteVertical Asymptote
f(x)=−6−16+4x\displaystyle {f{{\left({x}\right)}}}=\frac{{-{6}}}{{-{16}+{4}{x}}}
 
 
g(x)=−10x−9−5x−15\displaystyle {g{{\left({x}\right)}}}=\frac{{-{10}{x}-{9}}}{{-{5}{x}-{15}}}
 
 
f(x)=−7x2−17x+14\displaystyle {f{{\left({x}\right)}}}=\frac{{-{7}{x}^{{2}}-{1}}}{{{7}{x}+{14}}}
 
 
h(x)=x−x−1\displaystyle {h}{\left({x}\right)}=\frac{{x}}{{-{x}-{1}}}
 
 

Video 1 Shortcut Rules for Horizontal Asymptotes (HA)

Video 2 Why/How Vertical Asymptotes form.

Video 3 HA Case 1 Why/How HA form.

Video 4 HA Case 2 Why/How HA form.

Video 5 HA Case 3 Why/How HA form.

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