IB Maths AA SL 2.8 Reciprocal and rational functions Question Bank

Practise IB Maths AA SL 2.8 by identifying asymptotes, intercepts and graph features of rational functions.

Exam points

Find vertical and horizontal asymptotes and intercepts from a rational function.
Use algebraic or graphical transformations to sketch a reciprocal or rational function.
Check a rational-function solution against excluded values and asymptotic behaviour.

[Maximum number: 3]

Let $f(x)=\frac{2 x-6}{1-x}$ , for $x \neq 1$ .

(a)

For the graph of f

[ 3 ]

(i)

write down the equation of the vertical asymptote;

[ 1 ]

$\quad x=1$ (must be equation)

(ii)

find the equation of the horizontal asymptote.

[ 2 ]

valid approach
eg sketch, $\frac{2 x}{-1 x}$ , inputting large values of x, L'Hopital's rule y=-2 (must be equation)

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