Specialist2024 Exam 1 · Q3Tech-free6 marks

Partial fractions, turning point and graph of a rational function

Let $f : \R \setminus \{-1\} \to \R,\ f(x) = \dfrac{(x-1)^2}{(x+1)^2}$ .

Show that $A = 1$ , $B = -4$ and $C = 4$ .

1 mark

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The graph of $f$ has one turning point.

Find the coordinates of this turning point.

2 marks

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Sketch the graph of $y = f(x)$ on the set of axes below. Label the asymptotes with their equations and the axial intercepts with their coordinates.

Blank grid of Cartesian axes with x from about -6.5 to 4.5 and y from about -2.5 to 6.5, labelled at x = -6, -4, -2, 2, 4 and y = -2, 2, 4, 6, for sketching the graph of y = f(x).

3 marks

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