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}

. a. a Write an expression for

g(x)

in the form

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

. b. b Find the asymptotes of

y = g(x)

. c. c State the domain and range of

g(x)

. d. d Sketch

y = g(x)