IB Maths AA SL 2.8 Reciprocal and Rational Functions Questions

Practise finding asymptotes and intercepts of rational functions, sketching transformed graphs, and checking solutions against excluded values and asymptotic behaviour.

Exam points

Analyse reciprocal and rational functions, including asymptotes, intercepts and restrictions.
Solve equations or inequalities involving rational functions using complete evidence.

[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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IB Maths AA SL 2.8 Reciprocal and Rational Functions Questions question 1

Question (a)

Question (i)

Question (ii)