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Study SL 2.8—Reciprocal and rational functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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 Topic Practice

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Question 1

Question (a)

Question (b)

Question (c)