In Section 2.6, we talked about transformations of functions, including shifting, reflecting, and stretching/shrinking. The image below shows the graph of two functions

Discussion 5

In Section 2.6, we talked about transformations of functions, including shifting, reflecting, and stretching/shrinking. The image below shows the graph of two functions, f(x) (red) and g(x) (blue).

1. Explain how the graph of g(x) is obtained from the graph of f(x).
2. Tell how the the transformations in part (1) relate to the equation in part (2).

If 

, give an equation for g(x).

Discussion 6

In Section 3.2, we discussed polynomial functions and their graphs. Use the image below to respond to the following.

1. How many local extrema does the function have? State the number of local minimum points and local maximum points.
2. Based on part (1), what is the smallest degree this function could have?
3. Describe the end behavior of this function.
4. Based on part (3), is the degree of this function even or odd? Is the leading coefficient positive or negative?