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5.05 Graphing rational functions

Interactive practice questions

What is the resulting equation after we clear the fractions? Do not solve the equation.

$\frac{8}{\left(x+6\right)\left(x-6\right)}$8(x+6)(x6) $=$= $\frac{5}{x-6}+\frac{4}{x+6}$5x6+4x+6
$\left(x+6\right)\left(x-6\right)\times\frac{8}{\left(x+6\right)\left(x-6\right)}$(x+6)(x6)×8(x+6)(x6) $=$= $\left(x+6\right)\left(x-6\right)\left(\frac{5}{x-6}+\frac{4}{x+6}\right)$(x+6)(x6)(5x6+4x+6)
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Which of the following functions has a graph without a vertical asymptote?

Consider the function $f\left(x\right)=\frac{x}{x\left(x-5\right)}$f(x)=xx(x5)

Consider the function




Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.


Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

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