Common shifts and stretches on graphs involve moving a function f(x) around on a graph in accordance with the shift or stretch in question.
1. Y-Stretch: y = k * f(x)
The original graph is simply stretched along the y-axis by multiplying the function by a number. If k is less than 1, then the graph is squashed rather than stretched.
2. Y-shift: y = f(x) + a
This is where the whole graph is moved up or down the y-axis according to the value of a. a = 2 will move it 2 square up, a = -3 will move it 3 down.
3. X-Shift: y = f( x - a )
The whole graph slides to left or right according to the value of a. It is inversed - ie. a positive value for a moves the graph to the left, and vice-versa.
4. X-Stretch: Y = f(kx)
As with Y-stretch, but scrunches/stretches on the X-axis and go the "wrong way" as well a multiplier scrunches the graph, a divider stretches it out.