Which function does not have a vertical asymptote? A) y=(x) /(1-x²) . B) y=(5x) /(1-2x²) . C) y=(5x-1) /(3+x^2) . D) (5x) /(x+x²) .

Question

Which function does not have a vertical asymptote? A) y=(x) /(1-x²) . B) y=(5x) /(1-2x²) . C) y=(5x-1) /(3+x^2) . D) (5x) /(x+x²) .

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    0
    2021-09-11T05:08:08+00:00

    A function has a vertical asymptote x=a at point a, where the denominator becomes equal to 0.

    A. The denominator of the function f(x)=\dfrac{x}{1-x^2} turns into 0 at x=1 or x=-1. Then x=1 and x=-1 are two vertical asymptotes of this function.

    B. The denominator of the function f(x)=\dfrac{5x}{1-2x^2} turns into 0 at x=\sqrt{\frac{1}{2}} or x=-\sqrt{\frac{1}{2}}  Then x=\sqrt{\frac{1}{2}}  and x=-\sqrt{\frac{1}{2}}  are two vertical asymptotes of this function.

    C. The denominator of the function f(x)=\dfrac{5x-1}{3+x^2} never turns into 0, then this function hasn’t any asymptotes.

    D. The denominator of the function f(x)=\dfrac{x}{x+x^2} turns into 0 at x=0. Then x=0 is vertical asymptote of this function.

    Answer: correct choice is C.

    0
    2021-09-11T05:08:47+00:00

    Answer:

    C. y= (5x-1)/(3+x^2)

    Step-by-step explanation:

    a p e x

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