2007 H2 Mathematics Paper 1 Question 5

Graphs and Transformations

Answers

{y = 2 + \frac{3}{x + 2}}

Translate the graph of ${y=\frac{1}{x}}$ by ${2}$ units in the negative ${x\textrm{-}}$ axis direction.
Scale the resulting graph by a factor of ${3}$ parallel to the ${y\textrm{-}}$ axis.
Translate the resulting graph by ${2}$ units in the positive ${y\textrm{-}}$ axis direction.

Full solutions

By long division,

\begin{align*} y &= \frac{2 x + 7}{x + 2} \\ y &= 2 + \frac{3}{x + 2} \; \blacksquare \end{align*}

Translate the graph of ${y=\frac{1}{x}}$ by ${2}$ units in the negative ${x\textrm{-}}$ axis direction.
Scale the resulting graph by a factor of ${3}$ parallel to the ${y\textrm{-}}$ axis.
Translate the resulting graph by ${2}$ units in the positive ${y\textrm{-}}$ axis direction.

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