Question

Which of the following is false for
f(x) = (10x^3 - 10x^2 - 10x) / (2x^5 - 2x) ?

(a) The y-axis is not an asymptote of f(x).

(b) The x-axis is an asymptote of f(x).

(c) x = –1 is not an asymptote of f(x).

(d) x = 1 is an asymptote of f(x).

So, I took a quiz that had this question and I, of course, got it wrong. The first time that I took the quiz, it had a similar question to the one above and the second time I had taken it, it had this exact one. For the question above, I chose answer choice (a), because the first time I had chosen (c). Can someone PLEASE help me?

Answer 1

well if you factor the numerator and denominator you get

\[f(x) = \frac{10x(x^2 - x -1)}{2x(x^4 - 1)} = \frac{5(x^2 - x - 1)}{x^4 - 1}\]

so the function has vertical asymptotes at

x^4 = 1 or x = -1 and x = 1

Answer 2

there is a point of discontinuity at x = 0

since the degree of the denominator is greater than the degree of the numerator y = 0 is an asymptote so the x-axis is an asymptote

Answer 3

so the point of discontinity is the y- intercept (0, 5)

so I think the curve is