Parent graph: y=sin(x)

Vertical stretch/shrink: y=a*sin(x); stretchs/shrinks by a factor of a; if -1 < a < 1 then it is a shrink, otherwise it is a stretch
For example, y=2*sin(x) will stretch the graph vertically by a factor of 2.

Vertical flip: y=-sin(x)

Vertical shift: y=sin(x)+a; graph moves up by a units
For example, y=sin(x)+1 will shift the whole graph up 1 unit

Horizontal stretch/shrink (period stretch/shrink): y=sin(a*x) shrinks graph by factor of a; in other words, there are now a cycles every 2pi (or 360 degrees)
For example, y=sin(2x) will shrink the graph horizontally by a factor of 2

Horizontal flip: y=sin(-x)

Horizontal shift: y=sin(x-a); graph moves right by a units
For example, y=sin(x+pi) will shift the graph left by pi

Examples: (viewing window: xmin=pi, xmax=4pi, xscl=pi/2, ymin=-4, ymax=4, yscl=1; mode: radian)

Parent graph:

y=-3*sin(-2x-pi)
Here, the graph is first flipped horizontally, then shrunk horizontally by a factor of 2, shifted right by pi, then flipped vertically, then stretched vertically by a factor of 3.