Function transformations

The function $f(u) = (\sin u)e^{-u^2}$ is sketched on Figure 2.

Figure: Sketch of the function $f(u) = (\sin u)e^{-u^2}$.

For each of the parts (a) through (d), describe briefly what has happened to the function (compared to $f(u)$) using the following terms:

• translated (shifted)--left, right, up, down, how far;
• reflected--left-right, up-down;
• scaled--contracted, expanded, in what direction (left-right or up-down), by what factor.

Note: Use a plotting program if you wish or sketch by hand. You don't need to hand in the plots or sketches.

(a)

$f(u - 3)\;$;

(b)

$f(u/2)\;$;

(c)

$f(1-u/2)\;$;

(d)

$5 f(2u + 1)\;$