AnysiaA168985 AnysiaA168985
  • 04-11-2022
  • Mathematics
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State the domain of 1b, then determine the equation of any vertical asymptotes and/or coordinates of any holes in the graph of the function.

State the domain of 1b then determine the equation of any vertical asymptotes andor coordinates of any holes in the graph of the function class=

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LeticiaV431034 LeticiaV431034
  • 04-11-2022

We have

[tex]f(x)=\frac{2x^2+x}{x^2-5x+6}[/tex]

First we will factorize the function

[tex]f(x)=\frac{x(2x+1)}{\mleft(x-2\mright)(x-3)}[/tex]

The domain is

[tex]\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)[/tex]

In this case, we have two vertical asymptotes

x-2=0

x=2

x-3=0

x=3

ANSWER

The domain is

[tex]\: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: 3\mright)\cup\mleft(3,\: \infty\: \mright)[/tex]

The vertical asymtotes

x-2=0

x=2

x-3=0

x=3

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