VCE Maths Methods Functions Mini Test 4
Number of marks: 10
Reading time: 2 minutes
Writing time: 10 minutes
Section A – Calculator Allowed
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
The function \( f(x) = \log\left(\frac{a + x}{a - x}\right) \), where \( a \) is a positive real constant, has the maximal domain
- A. [–a, a]
- B. (–a, a)
- C. \( \mathbb{R} \setminus [–a, a] \)
- D. \( \mathbb{R} \setminus (–a, a) \)
- E. \( \mathbb{R} \)
The maximal domain of the function with rule \( f(x) = \sqrt{x^2 - 2x - 3} \) is given by
- A. \( (-\infty, \infty) \)
- B. \( (-\infty, -3) \cup (3, \infty) \)
- C. \( (-1, 3) \)
- D. [–3, 1]
- E. \( (-\infty, -1] \cup [3, \infty) \)
End of Section A
Section B – No Calculator
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Let \( f : \mathbb{R} \rightarrow \mathbb{R}, f(x) = x^2 - 4 \) and \( g : \mathbb{R} \rightarrow \mathbb{R}, g(x) = 4(x-1)^2 - 4 \).
a. The graphs of \(f\) and \(g\) have a common horizontal axis intercept at \((2, 0)\).
Find the coordinates of the other horizontal axis intercept of the graph of \(g\). 2 marks
b. Let the graph of \(h\) be a transformation of the graph of \(f\) where the transformations have been applied in the following order:
- • dilation by a factor of \( \frac{1}{2} \) from the vertical axis (parallel to the horizontal axis)
- • translation by two units to the right (in the direction of the positive horizontal axis)
a. Sketch the graph of \( f(x) = 2-\frac{3}{x - 1} \) on the axes below, labelling all asymptotes with their equations and axial intercepts with their coordinates. 3 marks
b. Find the values of \( x \) for which \( f(x) \leq 1 \). 1 mark
End of examination questions
VCE is a registered trademark of the VCAA. The VCAA does not endorse or make any warranties regarding this study resource. Past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au
