VCE Maths Methods Functions Mini Test 9
Number of marks: 10
Reading time: 2 minutes
Writing time: 15 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 graph of a function \(f\) is obtained from the graph of the function \(g\) with rule \(g(x) = \sqrt{2x-5}\) by a reflection in the \(x\)-axis followed by a dilation from the \(y\)-axis by a factor of \(\frac{1}{2}\).
Which one of the following is the rule for the function \(f\)?
- A. \(f(x) = \sqrt{5-4x}\)
- B. \(f(x) = -\sqrt{x-5}\)
- C. \(f(x) = \sqrt{x+5}\)
- D. \(f(x) = -\sqrt{4x-5}\)
- E. \(f(x) = -\sqrt{4x-10}\)
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 \(f: (0, \infty) \to R\), where \(f(x) = \log_e(x)\) and \(g: R \to R\), where \(g(x) = x^2+1\).
a.
i. Find the rule for \(h\), where \(h(x) = f(g(x))\). 1 mark
ii. State the domain and range of \(h\). 2 marks
iii. Show that \(h(x) + h(-x) = f((g(x))^2)\). 2 marks
b. Let \(k: (-\infty, 0] \to R\), where \(k(x) = \log_e(x^2+1)\).
i. Find the rule for \(k^{-1}\). 2 marks
ii. State the domain and range of \(k^{-1}\). 2 marks
End of examination questions
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