For each of the following families, show whether all the pots in the family are Unimodal. unimodal Thm.: Let f(x) be a paf, and let a be a number such that if a ≤ x=y, then flas = f(x) = ftyl and if a ≤ x ≤y, then f(a) = f(x) = f(y). a) uniform (a, b) b) gamma (x, A) c)^(1,0²)

For functions:f(x, y) = x − yg(x, y) = x2 + x − yDetermine whether the following sets are closed and bounded. If possible, make your graphs. a) GSg ∩ GIfb) GIg ∩ GSfc) CSg(1) ∩ CIf (2)d) CIg(1) ∩ CSf (2)

3. Consider f: I R. LetJ be an interval containing f(I). Let g: Consider the composition of f and g, i.e. gof: I-→ R. Show that: (1) If both f and g are strictly monotone increasing, then g of: I→R is strictly monotone increasing. (2) If both f and g are strictly monotone decreasing, then gof: I→R is strictly monotone increasing. (3) If one of f and g is strictly monotone increasing and the other is strictly monotone decreasing, then gof:I →R is strictly monotone decreasing. J R.

please answer b) c) and d)