Warm-Up: Composite Functions
Composite Function Review and Exploration
Below is a dynagraph which contains 3 sliders: The first contains the value of x. The second contains the value of f(x). The third contains the value of f(g(x)).
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. What function did you use for f(x)? How about g(x)? Find f(g(x)) at a certain x value.