Sketch a graph of a single function that has these properties.
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Quizplus · Accepted Answer

A function with a vertical asymptote at x=3 means the function approaches positive or negative infinity as x approaches 3 from either side. A function with a hole at x=2 means there is a point at (2,3) that is missing from the graph. We can create such a function by taking a rational function with a vertical asymptote at x=3 and cancelling out the common factor in the numerator and denominator at x=2 to create a hole. One possible function that satisfies these conditions is:

$f(x) = \frac{(x-2)(x-4)}{(x-3)^2}$

This function has a vertical asymptote at x=3 and a hole at x=2.

Sketch a Graph of a Single Function That Has These