1. For each of the following situations, what kind of function might you choose to encode the dependence? Give reasons for your answer. (10) a. Temperature of a cup of hot tea sitting in a room as a function of time. b. Population of cicadas as a function of time. (Several types of cicada are well-known for a 17-year breeding cycle.) c. d. e. Temperature of the ocean depending on lattitude. Cost of oil depending on time. Rate of photosynthesis depending on the intensity of the sunlight. 2. For each of the following functions, express the function as the composition of two other functions. (8) a. C. 1+ +1 1 tan X (x+1) 1 + x 1 X d. (sin(x+1)) + 4 sin(x + 1) + 3 te 3. For the following pairs of functions f and g, calculate fog and go f. Simplify the expressions for the composition as much as you can. Then state the domains of fog and go f. (15) a. f(x) = cos x and g(x) = x. f(x) = tan x and g(x) = x+3 b. c. f(x) = x 4x + 1 and g(x) = x 7. 4. Invert the following functions on the given domain. (You may assume the function is monotonic on the given domain). State the domain of the inverse. (12) a. f(x) = x +7 on the domain (0, ). b. f(x) = ex+4 on the domain R. f(x) = n(+3) on the domain (-2,00). 1 c.