contestada

find the formula for a rational function that satisfies all of the following. its x-intercept is (-3,0). it has a vertical asymptotes, namely x=-1 and x=0. it has one horizontal asymptote, namely y=3

Respuesta :

Let that be

[tex]\\ \rm\Rightarrow y=\dfrac{a(f(x))}{g(x)}[/tex]

Two vertical asymptotes at -1 and 0

[tex]\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x(x+1)}[/tex]

If we simply

[tex]\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x^2+1}[/tex]

  • Denominator has degree 2
  • Numerator should have degree as 2 and coefficient as 3 inorder to get horizontal asymptote y=3 means the quadratic equation should contain 3x²
  • But there should be a x intercept at -3 so one zeros should be -3

Find a equation

  • 3x²+9x

Find zeros

  • 3x²+9x=0
  • 3x(x+3)=0
  • x=0,-3

Horizontal asymptote

  • 3x²/x²
  • 3

So our equation is

[tex]\\ \rm\Rightarrow y=\dfrac{3x^2+9x}{x(x+1)}[/tex]

Graph attached

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