Problem

The function

g(x)

results when

y = \frac{1}{x}

is transformed by a translation of

\begin{pmatrix} -1 \\ 3 \end{pmatrix}

, followed by a horizontal stretch with scale factor

\frac{1}{2}

. a. Write an expression for

g(x)

in the form

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

. b. Find the asymptotes of

y = g(x)

. c. State the domain and range of

g(x)

. d. Sketch

y = g(x)