# 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)(x−6)​ $=$= $\frac{5}{x-6}+\frac{4}{x+6}$5x−6​+4x+6​ $\left(x+6\right)\left(x-6\right)\times\frac{8}{\left(x+6\right)\left(x-6\right)}$(x+6)(x−6)×8(x+6)(x−6)​ $=$= $\left(x+6\right)\left(x-6\right)\left(\frac{5}{x-6}+\frac{4}{x+6}\right)$(x+6)(x−6)(5x−6​+4x+6​)
Easy
Approx 3 minutes

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

$y=\frac{15x}{5x^2+4}$y=15x5x2+4

### Outcomes

#### MGSE9-12.F.IF.7

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

#### MGSE9-12.F.IF.7d

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