Composite Functions: Linear to Trigonometric

Open a new graphing window.

Define linear function f1 in terms of a variable. Press Enter to graph it.

Now define trigonometric function f2 in terms of f1. Press Enter to graph it.

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

Define function f3 in terms of f2 so that it results in a horizontal shift.

Define function f4 in terms of f3 so that it results in a composite of two trigonometric functions.

Change function f1 and see how the correspond functions change

while they maintain their relative distance from f1.