The function results when is transformed by a vertical stretch with scale factor

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The function

g(x)

results when

y=\frac{1}{x}

is transformed by a vertical stretch with scale factor

3

, followed by a translation of

\begin{pmatrix}1\\-1\end{pmatrix}

. (1) a) Write an expression for

g(x)

in the form

g(x)=\frac{ax+b}{cx+d}

. (2) b) Find the asymptotes of

y=g(x)

. (3) c) State the domain and range of

g(x)

. (4) d) Sketch

y=g(x)