IB Maths AA HL 2.8 Reciprocal and rational functions with parameters Question Bank

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

Exam points

Derive asymptotes, holes and intercepts while tracking excluded domain values.
Analyse how a parameter changes the graph, range or number of intersections.
Evaluate a rational-function model using algebraic simplification and asymptotic 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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SL 2.8—Reciprocal and rational functions question 1

Question (a)

Question (b)

Question (c)