Singapore GCE A-Level · H2 Mathematics

Functions, Graphing Techniques and Transformations

6 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 6 questions

The function $f$ is defined by $f : x \mapsto \frac{2 x + 1}{x - 3}$ for $x \in R, x > 3$ . Find the rule and domain of the inverse function $f^{- 1}$ .
The curve $C$ with equation $y = f (x)$ undergoes a transformation: first a stretch by factor $2$ parallel to the $x$ -axis, followed by a translation of $3$ units in the negative $x$ -direction. What is…
Find all asymptotes of the rational curve $y = \frac{2 x ^{2} - 5 x + 1}{x - 2}$ .
Let $f (x) = x^{2} - 4 x + 7$ for $x \in R$ . What is the least value of $k$ such that the restricted function $g (x) = f (x)$ for $x \geq k$ has an inverse?
Given functions $f (x) = ln (x - 1)$ for $x > 1$ and $g (x) = e^{2 x} + 1$ for $x \in R$ , find the rule and range of the composite function $f g (x)$ .
The curve $y = \frac{a x + b}{c x + d}$ has asymptotes $x = 3$ and $y = 2$ , and passes through the point $(1, 0)$ . Find the value of $\frac{b}{a}$ .

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