Composite Functions: Linear to Polynomial

Open a new graphing window. Define linear function f1 in terms of a variable.

Press Enter to graph it.

Now define polynomial function f2 in terms of f1.

Press Enter to graph it.

Notice that the graph of f2 is the graph of a polynomial function.

Define function f3 in terms of f2 so that it results in a shift up by 1.

Define function f4 in terms of f2 so that it results in a horizontal shift.

Change function f1 and see how the corresponding functions change,

while they maintain their relative distance from f1.