Integer constants of a rational function from two points, and the stretch and translation from the reciprocal graph
Integer constants of a rational function from two points, and the stretch and translation from the reciprocal graph
8 marks
The diagram below shows part of the graph of \(y=\frac{Ax+B}{x+3}\), for \(x\in\mathbb{R}\), \(x\neq-3\), where \(A\) and \(B\) are integers. The points \(P(-6,1)\) and \(Q(-1,6)\) lie on the graph.
- Find the value of \(A\) and the value of \(B\).[3]
- Describe fully two transformations which, applied one after the other, map the graph of \(y=\frac1x\) onto the graph of \(y=\frac{Ax+B}{x+3}\).[5]
Solution:
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Answer:(a) \(A=3,\ B=15\) (b) a stretch parallel to the \(y\)-axis with scale factor \(6\), followed by a translation by \(\begin{pmatrix}-3\\ 3\end{pmatrix}\)
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