<p>This last problem gives an example of another technique on my list of Advanced Strategies.</p>
<p>Basic Transformations:</p>
<p>Given a function f(x) and a positive number c, we have the following basic transformations.</p>
<p>f(x) + c : vertical shift up c units
f(x) – c : vertical shift down c units
f(x – c) : horizontal shift right c units
f(x + c) : horizontal shift left c units
-f(x) : reflection in x-axis
f(-x) : reflection in y-axis
cf(x) : vertical expansion if c > 1, vertical compression if 0 < c < 1
f(cx) : horizontal expansion if 0 < c < 1, horizontal compression if c > 1</p>