1. (a) Carefully graph the piecewisedened function 5531 1:c1 (b) Determine the domain and range of f 2. Given the function f (3:) = 23: + 4, apply the following transformations (in the given order) and write an equation for the final transformed graph: Shrink the graph vertically by a factor of %, shift upward 3 units, and reect the graph in the yaxis. 3. Let h(:1:) = 2:33 - 5:32 + 3x + 7. Express h(x) in the form 12(3)) = (:1: 2)q(:v) + 1', where (301:) is a polynomial and r is a number. Use the Remainder Theorem to check that you have the correct remainder. 4. Using algebraic methods, nd the solution sets for the following: 3 1 (a) f: > 2. (b) 502-1235820. 5. Solve the following equations algebraically (a) 10m + 2) + 10g2(3) = 1032(27) (M(WF5Q+6=0 6. The half-life of radium-226 is 1600 years. Suppose we have a 22 mg sample. (a) Find the relative decay rate r. (b) Use 7\" above to nd a function that models the mass remaining after 72 years. (c) How much of the sample will remain after 4000 years? 7. Two observers simultaneously measure the angle of elevation of a helicopter. One angle is measured as 25, the other as 40. If the observers are 100 feet apart and the blimp lies over the line joining them, how high is the blimp? 8. A ship leaves a harbor. It travels 35 miles due east and then adjusts its course 40 degrees northward. After traveling 45 miles in that direction, how far is the ship from its point of departure? 1 9. Find the exact value of the expression sin -(2 cos(?)) 10. Let cos(0) = 2 for ,