For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x minus five divided by the quantity x squared minus one

Step-by-step explanation:

The function is:

             x - 5

f(x) =

            x^2 - 1

Horizontal asymptote:  observe that as x grows towards infinity, the function (and graph) approaches y = 0.  This is the horizontal asymptote.

Vertical asymptote:  These occur whenever the denominator of a rational function becomes zero.  Here the vertical asymptotes are  x = ± 1.

more detail

step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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