This set of 20 task cards presents students with graphical information about functions f and g. Then students are asked to consider several composite functions

1. f(g(x))

2. g(f(x))

3. f(x^2)

4. f(-x^2)

5. f(f(x))

6. g(g(x))

Students try to decide if these functions are increasing, decreasing or neither at a given value of x or if the derivative is positive, negative or zero at a given value of x.

Students must answer questions like this on the ap calculus exam.

For all questions students must justify their answers.

Complete solutions to all problems are included.