Consider the function f (x) = x5 x + b where b is a real constant. Use Desmos to graph this function with a slider for b. Guiding Questions: 1. What do you notice about how the slope of the function changes with ? What does this tell us about how addition or subtraction of constants impact the behavior of functions? How does this related to the graph transformations you reviewed in week 1 of the course? 2. Now that you have a sense for the function's behavior, pick two distinct points a, b in the function's domain such thatf (a) = f (b). If the MVT holds, what feature must be present in the function for some t with a < x < b How can we use this observation to get a better sense for functions more generally