Question: A student observes that the function f(x) = 1/x + 2, x 0, has a change of sign on the interval [1, 1]. The

A student observes that the function f(x) = 1/x + 2, x ≠ 0, has a change of sign on the interval [−1, 1]. The student writes: y = f(x) has a vertical asymptote within this interval so even

By means of a sketch, or otherwise, explain why the student is incorrect.

y = f(x) has a vertical asymptote within this interval so even though there is a change of sign, f(x) has no roots in this interval.

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