Specialist2023 Exam 1 · Q1Tech-free4 marks

Rational function with an oblique asymptote

Consider the function $f$ with rule $f(x) = \dfrac{x^2 + x - 6}{x - 1}$ .

Show that the rule for the function $f$ can be written as $f(x) = x + 2 - \dfrac{4}{x - 1}$ .

1 mark

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Sketch the graph of $f$ on the axes below, labelling any asymptotes with their equations.

Blank Cartesian axes with a grid, x from -5 to 5 and y from about -5 to 10, for sketching the graph of f.

3 marks

Hints, answer checking and worked solutions come with a Season Pass.