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Tyro
Asked: 2021-04-09T14:44:03+00:00 In: ,

Rational function

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find the x and y intercept of 

f(x)= x^2 -15 /x^2-2x-3

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  2. acedstud
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    The x-intercepts of a function, f(x), are the values of x when f(x)=0.

    Given f(x)=\dfrac{x^2 -15}{x^2-2x-3}.

    Letting f(x)=0, we have \dfrac{x^2 -15}{x^2-2x-3}=0\Rightarrow x^2-15=0        {\because multiplying both sides by the denominator.]

    Adding 15 to both sides and then taking the square root of both sides, we have x^2=15\Rightarrow x=\pm\sqrt{15}.

    Therefore, the x-intercepets of the function are at x=\pm\sqrt{15}.

     

    The y intercepts of a function are the values of f(x) when x=0. Thus, equating x=0 in the function, we have f(0)=\dfrac{0^2 -15}{0^2-2(0)-3}=\dfrac{-15}{-3}=5.

    Therefore, the y intercept is at y=5.

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