Transformations of Graphs - Reciprocal Graph, \(y=\frac{1}{f(x)}\)
Transformations of Graphs - Reciprocal Graph, \(y=\frac{1}{f(x)}\)
9 marks
The diagram below shows the graph of \(y = \mathrm{f}(2x)\). The graph has a turning point at \((2, 0)\), and asymptotes with equations \(x = 0\) and \(y = k\).
- State a single transformation that will transform the graph of \(y = \mathrm{f}(2x)\) onto the graph of \(y = \mathrm{f}(2x + 4)\). Hence sketch the graph of \(y = \mathrm{f}(2x + 4)\).[3]
On separate clearly labelled diagrams, sketch the graphs of
- \(y = \frac{1}{\mathrm{f}(2x)}\)[3]
- \(y = -\mathrm{f}(|x|)\)[3]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) Translation 2 units left; minimum \((0,0)\), asymptotes \(x=-2,y=k\). (b) Asymptotes \(x=2,y=\dfrac1k\); excluded point \((0,0)\). (c) Maxima \((\pm4,0)\); asymptotes \(x=0,y=-k\); even graph.
Need help? Join our IP Math tuition programme.
Learn more