Mathematico | Mathematico

Below is a sketch of

y = \frac{1}{(x - 1) (x + 2)}

Hence, sketch

y = \frac{1}{2 (2 x - 1) (x + 1)}

Let

f (x) = \frac{1}{(x - 1) (x + 2)}

be the original function, which is sketched for us.

Write the new function as

\frac{1}{2 (2 x - 1) (x + 2)} = \frac{1}{(2 x - 1) (2 x + 2)}

(we have put the $2$ into the second bracket).

Based on the hint above, $x$ has been replaced with $2 x,$ so we have to sketch

y = f (2 x)

which is an enlargement, scale factor $\frac{1}{2}$ , parallel to the $x$ axis.