Functions Galore!

DO NOT USE A CALCULATOR!

1. Define a @ b as a @ b = a^2 - b. Calculate 3 @ (5 @ 6).

2. Define $(a,b,c) to be $(a,b,c) = a(b-c). Calculate $($(0,8,6),$(6,3,4),$(1,7,5)).

3. Graph y = -2sqrt(x-3)+1.

4. In a country, population is determined as a function of time. Officials produce population patterns by using the function P(t) = 0.5t^2 + 0.358t. Determine the population (to the nearest whole number) after 110 years of growth. (Hint: 110=100+10)

Pythagorean Theorem Extended

If a < b, then 3^2 + 4^2 + 5^2 + 12^2 = a^2 + b^2 is represented by FOUR ordered pairs (a,b). What is the area of the figure that is bounded by these four ordered pairs if they were graphed on a Descartes grid?