VCE Methods Functions Application Task 2
Number of marks: 7
Reading time: 1 minute
Writing time: 10 minutes
Section B – Calculator Allowed
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 \( f : \mathbb{R} \rightarrow \mathbb{R} \), \( f(x) = x(x - 2)(x + 1) \). Part of the graph of \( f \) is shown below.
a. State the coordinates of all axial intercepts of \( f \). 1 mark
Let \(f: \mathbb{R} \to \mathbb{R}\), \(f(x) = a(x+2)^2(x-2)^2\), where \(a \in \mathbb{R}\). Part of the graph of \(f\) is shown below.
a. Show that \(a = \frac{1}{4}\). 1 mark
b. Express \(f(x) = \frac{1}{4}(x+2)^2(x-2)^2\) in the form \(f(x) = \frac{1}{4}x^4 + bx^2 + c\), where \(b\) and \(c\) are integers. 1 mark
a. Express \(\frac{2x+1}{x+2}\) in the form \(a + \frac{b}{x+2}\), where \(a\) and \(b\) are non-zero integers. 2 marks
b. Let \(f: R \setminus \{-2\} \to R, f(x) = \frac{2x+1}{x+2}\).
i. Find the rule and domain of \(f^{-1}\), the inverse function of \(f\). 2 marks
End of examination questions
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