Sketch a graph of the fundamental function y = x^2.

Using arrows to indicate the stretching or shifting of the function, show how the graph is transformed by each of the following:

• A vertical stretch by factor 3.
• A horizontal shift of 1.75 units.
• A vertical shift of 1.25 units.

Using the knowledge that a function y = f(x) is transformed to the function y = A f(x) by a vertical stretch by factor A, to y = f(x-h) by a horizontal shift of h units, or to y = f(x) + k by a horizontal shift of k units, what give the form of each transformed function.