VCE Methods Logs & Exponentials Application Task 1
Number of marks: 4
Reading time: 1 minute
Writing time: 6 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 \( f : \mathbb{R} \rightarrow \mathbb{R} \), \( f(x) = e^x + e^{-x} \) and \( g : \mathbb{R} \rightarrow \mathbb{R} \), \( g(x) = \frac{1}{2} f(2-x) \).
a. Complete a possible sequence of transformations to map \( f \) to \( g \). 2 marks
- Dilation of factor \( \frac{1}{2} \) from the x-axis.
Let \(q(x) = \log_e(x^2 - 1) - \log_e(1 - x)\).
a. State the maximal domain and the range of \(q\). 2 marks
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
