Play around with the dynagraph by dragging the red point to change the value of x. What do you notice? What do you wonder? Share with a partner and write at least one notice and wonder below.

When x=0, what does f(x) equal, according to the dynagraph? What does f(g(x)) equal? Does this make sense given the functions f(x)=x^2 and g(x)=sin(x)? Write your answer below and confirm with a partner.

Try another value of x. What does f(x) equal? What does g(f(x)) equal? Find values on the dynagraph. Do they make sense given the functions f(x)=x^2 and g(x)=sin(x)? Write your answer below and compare with a partner.

Notice on the applet that you can type your own functions into f(x) and g(x). Create your own composite function and evaluate f(g(x)) at any x value. Ensure the value on the dynagraph is equivalent to the value you get when you evaluate the composite function by hand or with a calculator. [br][br]What function did you use for f(x)? How about g(x)? Find f(g(x)) at a certain x value.