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Home > PC > Chapter 10 > Lesson 10.1.1 > Problem 10-11

10-11.

Find all asymptotes and holes for the function .

Start by factoring the numerator and denominator and simplifying.

Vertical asymptotes and holes occur when the denominator is equal to .

Horizontal asymptotes are found by considering what happens to the function as .

Identify the dominant terms and simplify.

Check your answer by graphing.

3 decreasing curves, left coming from left below y = 2, going to negative infinity left of x = negative 2, center coming from infinity right of x = negative 2, changing concavity at about (1, comma 2.5), going to negative infinity left of x = 3, right, coming from infinity right of x = 3, going to the right above y = 2.