Composite Functions: Linear to Rational

Open a new graphing window.

Define linear function f1 in terms of a variable.

Press Enter to graph it.

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

Notice that the graph of f2 is the graph of a rational function with asymptotes x and y equal to zero.

Define function f3 in terms of f1 so that it results in a rational function

with asymptotes x = 2 and y = 0.

Define function f4 in terms of f1 so that it results in a rational function

with asymptotes x = 0 and y = 3.

Change function f1 and see how the corresponding functions change

while they maintain their relative distance from f1.