Exercises for Question Type 1: Finding the horizontal and vertical asymptotes of simple rational functions

Question 1

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{4 x ^{3} - x}{2 x ^{3} + 5}$

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Question 2

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{2 x}{x ^{2} - 1}$ .

[4]

Question 3

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{3 x ^{2} + 1}{x ^{2} - 4}$

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Question 4

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{x + 2}{x - 3}$ .

[4]

Question 5

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{x ^{2} - 9}{x ^{2} + 3 x - 10}$ .

[4]

Question 6

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{5 x + 8}{7 x + 9}$

[4]

Question 7

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{2 x ^{2} - 5 x + 3}{4 x ^{2} + x - 2}$ .

[4]

Question 8

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{4}{x + 5}$

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Question 9

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{- 3 x ^{4} + 2}{x ^{4} - 16}$

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Question 10

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{6 x - 4}{2 x + 3}$

[4]

Question 11

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{x ^{2} + 2 x + 1}{x ^{2} - 1}$

[4]

Question 12

Skill question

Find the horizontal and vertical asymptotes of $f (x) = \frac{5 x ^{2} + 2 x - 1}{3 x ^{2} - 12}$

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IB Mathematics Analysis and Approaches Question Type 1: Finding the Horizontal and Vertical Asymptotes of Simple Rational Functions Exercises