1. We know that order matters when applying transformations to a function ?=??(?(?-?))+?. Most students conclude that we need to complete compressions, expansions, and reflections before we do the translations. Is there some flexibility in that order? Explain
2. Susan and Jason were both given the function ?=(?)^1/2. Susan, compresses the function vertically by a factor of 1/2. Jason expands it horizontally by 4. They get the same result. Explain why. All horizontal expansions can be expressed as vertical compressions. Find two different functions, beyond the square root function, where this statement is true andone function where it is not true. Justify your answer.
3. Make a sketch of a polynomial function, p(x), with the following characteristics: roots at x = 1, x = -3, and x = 4, and a y-intercept of -4. Find the equation of your graphed polynomial? Is your equation the only possible answer? Explain.
4. Related species living in the same area often evolve in different sizes to minimize competition for food and habitat. Here are the masses of eight species of fruit pigeon found in New Guinea, ranked from smallest to largest. (Source: Burton, 1998) Use our knowledge of functions to find the equation of a function that will allow you to estimate the mass of a hypothetical fruit pigeon of size rank 0. Explain.

\f\f