Mathematics

Question

Which graph represents the function f(x)= 2x-1/x-1
Which graph represents the function f(x)= 2x-1/x-1
Which graph represents the function f(x)= 2x-1/x-1

2 Answer

  • The third answer is the right one. Or C
  • To determine which graph represents the function [tex]f(x)=\dfrac{2x-1}{x-1}[/tex] make following steps:

    1. The vertical asymptote is [tex]x=1.[/tex]

    2. Simplify the function

    [tex]f(x)=\dfrac{2x-1}{x-1}=\dfrac{2x-1-1+1}{x-1}=\dfrac{2(x-1)+1}{x-1}=2+\dfrac{1}{x-1}.[/tex]

    Then the horizontal asymptote is [tex]y=2.[/tex]

    Only option C contains graph with such asymptotes.

    Answer: correct choice is C

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