The function results when is transformed by a translation through followed by a…

Other · Multi-part · AoPS · Mathematics · Graphing Functions · Basics

Problem

The function

g(x)

results when

y = \frac{1}{x}

is transformed by a translation through

\begin{pmatrix} -1 \\ 2 \end{pmatrix}

followed by a reflection in the

y

-axis. (1) Write an expression for

g(x)

in the form

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

. (2) Find the asymptotes of

y = g(x)

. (3) State the domain and range of

g(x)

. (4) Sketch

y = g(x)