One way to visualize a composition of functions is to use a web graph. Here's how you evaluate f (g(x)) for any value of x, using a web graph:
Choose an x-value. Draw a vertical line from the x-axis to the function g(x). Then draw a horizontal line from that point to the line y = x. Next, draw a vertical line from this point so that it intersects f (x). Draw a horizontal line from the intersection point to the y-axis. The y-value at this point of intersection gives the value of f (g(x)).
Choose two functions f (x) and g(x). Use web graphs to find f (g(x)) for several values of x. Why does this method work?