1. Stretches ...
and some
reflections.
Ballet stretch

2. Translations y = ƒ(x - a) + b
The role of parameter a: Examples
a > 0 the graph shifts right a units.
- the x-coordinates are increased a
units.
a < 0 the graph shifts left a units.
- the x-coordinates are decreased a
units.
WARNING: watch the sign of a
The role of parameter b:
b > 0 the graph shifts up b units.
- the y-coordinates are increased b
units.
b < 0 the graph shifts down b units.
- the y-coordinates are decreased b
units.

3. Stretches ... (and a wee bit about reflections)
Let's start with a circle ...
Let's look at some graphs ... We'll head over to fooplot.com ...

5. Stretches and Compressions:
DICTIONARY
The role of parameter a:
Examples
a > 1 the graph of ƒ(x) is stretched vertically.
0 < |a| < 1 the graph of ƒ(x) is compressed
vertically.
- the y-coordinates of ƒ are multiplied by a.
The role of parameter b:
b > 1 the graph of ƒ(x) is compressed
horizontally.
(Everything quot;speeds upquot;)
0<|b|<1 the graph of ƒ(x) is stretched
horizontally. (Everything quot;slows downquot;)
- the x-coordinates are multiplied by .

8. Find two equations for this graph, one in sine, the other in cosine.