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.

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