IB Maths AA HL Sl 2 8 Reciprocal and Rational Functions Questions

Practise IB Maths AA HL 2.8 by analysing parameterised rational functions and their asymptotes, discontinuities and ranges.

Exam points

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

[Maximum number: 5]

Consider the function defined by $f(x)=\frac{k x-5}{x-k}$ , where $x \in \mathbb{R} \backslash\{k\}$ and $k^{2} \neq 5$ .

(a)

State the equation of the vertical asymptote on the graph of y=f(x).

[ 1 ]

(b)

State the equation of the horizontal asymptote on the graph of y=f(x).

[ 1 ]

(c)

Sketch the graph of y=f(x), stating clearly the equations of any asymptotes and the coordinates of any points of intersections with the coordinate axes.

[ 3 ]

attempt to draw both branches of a rectangular hyperbola M1
x=3 and y=3
A1
$\left(0, \frac{5}{3}\right)$ and $\left(\frac{5}{3}, 0\right)$

Figure for Answer to Question (c) — IB Maths AA HL

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IB Maths AA HL Sl 2 8 Reciprocal and Rational Functions Questions question 1

Question (a)

Question (b)

Question (c)