Enlargement of graphs

The graph of a function can be stretched or squashed to give a new shape. We call this type of transformation an enlargement (even if the graph is being squashed, we still call it an enlargement).

Just like with translations, there is a relationship between the enlargement and the equation of the graph, and the enlargement can be in the horizontal or the vertical direction (or both!).

Let's take a look at an example to see how all of this works - click next to get going!

The function $f$ is defined by

f (x) = (x + 1) (x - 2)^{2}, - 1 \leq x \leq 3

You are given that $f$ has a local maximum at $x = 0.$

Complete the tables below

\begin{array}{rcccccc} x & - 1 & 0 & 1 & 2 & 3 \\ (x + 1) (x - 2)^{2} \end{array}

\begin{array}{rcccccc} x & - \frac{1}{2} & 0 & \frac{1}{2} & 1 & \frac{3}{2} \\ (2 x + 1) (2 x - 2)^{2} \end{array}

\begin{array}{rcccccc} x & - 2 & 0 & 2 & 4 & 6 \\ (\frac{x}{2} + 1) (\frac{x}{2} - 2)^{2} \end{array}

\begin{array}{rcccccc} x & - 1 & 0 & 1 & 2 & 3 \\ (x + 1) (x - 2)^{2} \\ 2 (x + 1) (x - 2)^{2} \\ \frac{1}{2} (x + 1) (x - 2)^{2} \end{array}

Sketch each curve. What do you notice?