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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IB Analysis and Approaches |
The function \( f \) is defined by \( f(x) = \frac{5x + 5}{3x - 6} \) for \( x \in \mathbb{R}, x \neq 2 \).
(a) Find the zero of \( f(x) \).
(b)For the graph of \( y = f(x) \), write down the equation of the asymptotes;
(c) Find \( f^{-1}(x) \), the inverse function of \( f(x) \).
2. | IB Analysis and Approaches |
The function \(f\) is defined by:
$$f(x) = \frac{4x+2}{x+1}, \quad \text{ where } x \in \mathbb{R}, x \neq -1 $$(a) Write down the equation of the vertical asymptote of the graph of \(f\).
(b) Write down the equation of the horizontal asymptote of the graph of \(f\).
(c) Find the coordinates of the \(x\)-axis and \(y\)-axis intercepts.
(d) Sketch the graph of \(f\).
3. | IB Analysis and Approaches |
A function \(f\) is defined by \(f(x) = 2 + \dfrac{1}{3-x}, \text{ where } x \in \mathbb{R}, x \neq 3.\)
The graph of \(y=f(x)\) has a vertical asymptote and a horizontal asymptote.
(a) Write down the equation of the horizontal asymptote;
(b) Write down the equation of the vertical asymptote;
Find the coordinates of the point where the graph of \(y\) intersects:
(c) the y-axis;
(d) the x-axis.
4. | IB Standard |
Let \(f(x) = \frac{9x-3}{bx+9}\) for \(x \neq -\frac9b, b \neq 0\).
(a) The line \(x = 3\) is a vertical asymptote to the graph of \(f\). Find the value of b.
(b) Write down the equation of the horizontal asymptote to the graph of \(f\).
(c) The line \(y = c\) , where \(c\in \mathbb R\) intersects the graph of \( \begin{vmatrix}f(x) \end{vmatrix} \) at exactly one point. Find the possible values of \(c\).
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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
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