If x=1 is the vertical asymptote and y=-3 is the horizontal asymptote for the graph of the function f
which of the following could be the equation of the curve
A.f(x)=(-3x^2)/(x-1)
B.f(x)=-3(x-1)/(x+3)
C.f(x)=-3(x^2-1)/(x-1)
D.f(x)=-3(x^2-1)/(x-1)^2
2 answers
The answer is D but can someone explain to me why it is?
x=1 is the vertical asymptote
so you need a fraction with (x-1) in the denominator
since division by zero is undefined, and if the numerator is not zero, there will be a vertical asymptote there.
and y=-3 is the horizontal asymptote
Since there is a horizontal asymptote, the degree of the numerator is equal to that of the denominator.
Since the asymptote is at y = -3, the ratio of the leading coefficients is -3.
So, an easy function would be 3(x-k)/(x-1) where k≠1
That is not one of the choices, but D is the only choice which has the required factors.
so you need a fraction with (x-1) in the denominator
since division by zero is undefined, and if the numerator is not zero, there will be a vertical asymptote there.
and y=-3 is the horizontal asymptote
Since there is a horizontal asymptote, the degree of the numerator is equal to that of the denominator.
Since the asymptote is at y = -3, the ratio of the leading coefficients is -3.
So, an easy function would be 3(x-k)/(x-1) where k≠1
That is not one of the choices, but D is the only choice which has the required factors.
1 answer