Exercises for Question Type 3: Graphing different rational functions, including the intercepts and the asymptotes

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Exercises for Question Type 3: Graphing different rational functions, including the intercepts and the asymptotes - IB

Question 1

Sketch the graph of the function f (x) = \frac{5 x + 8}{7 x + 9} . Find its domain, x-intercept, y-intercept, vertical asymptote, and horizontal asymptote.

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Question 2

Consider the function f (x) = \frac{x ^{2} + 4 x + 3}{x + 1} . Find the domain, intercepts, and any holes or asymptotes. Hence, sketch the graph of f .

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Question 3

Parts Part 1 [8m] Sketch the graph of the function f (x) = \frac{4 x ^{2} + 2 x - 3}{2 x - 1} . Find its intercepts, vertical asymptote, and oblique asymptote.

Sketch the graph of the function f (x) = \frac{4 x ^{2} + 2 x - 3}{2 x - 1} . Find its intercepts, vertical asymptote, and oblique asymptote.

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Question 4

For f (x) = \frac{x ^{2} - 4}{x - 2}, find any holes, intercepts, and asymptotes, then sketch the graph.

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Question 5

For the function f (x) = \frac{2 x ^{2} - 3 x + 1}{x - 1}, determine the intercepts and the equations of the vertical and oblique asymptotes. Sketch the graph of f (x) .

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Question 6

For f (x) = \frac{3 x ^{2} - 5 x + 2}{x - 2}, determine intercepts, asymptotes (vertical and oblique), and sketch the graph.

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Question 7

Sketch f (x) = \frac{x ^{2} - 9}{x ^{2} - 4} Determine all intercepts, vertical asymptotes, horizontal asymptote, and any holes.

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Question 8

Sketch the graph of f (x) = \frac{2 x + 3}{x - 1} . State the coordinates of the axes intercepts and the equations of all asymptotes.

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Question 9

Sketch f (x) = \frac{x ^{2} + x - 6}{x + 3} . Identify the domain, holes or asymptotes, and intercepts.

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Question 10

Sketch the graph of f (x) = \frac{5}{x + 2} . State its intercepts and asymptotes.

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Question 11

Find the domain, intercepts, and asymptotes of the function f (x) = \frac{3 x - 1}{2 x + 5} . Sketch the graph of f .

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Question 12

Sketch the graph of f (x) = \frac{x ^{3} - 1}{x ^{2} - 1} . Identify the domain, holes, vertical asymptotes, oblique asymptote, and axes intercepts.

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IB Mathematics Analysis and Approaches Question Type 3: Graphing Different Rational Functions, Including the Intercepts and the Asymptotes Exercises