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PART A – Graphing Calculator is allowed.

Write the answer on the lines, at the right.

Show your work under the question and the answer in the right.

1. Determine the remainder when 2x2 + x +4 is divided by (x-1) [2 K/U]

2. Find the equation of the function y = f (x) that has zeros -1, 2, and y-intercept -4 and express it in the form y = ax2 + bx + c .

Write it  as y = ax2  + bx + c . [3 K/U]

3. Determine the instantaneous rate of change for y = (x - 2)2 x3   at x = 1. [3 K/U]

4. Using f(x) = x3 - 5x2  + 7x - 3 , determine the slope of the secant passing through f(1) andf(1.05) . [3 K/U]

5. A taxi company charges $3.00 for the first 0.25 km (or part of a quarter kilometer), and $0.25 for each additional 0.1 km (or part), up to a maximum of 2 km.

List all discontinuities of the function. [2 T]

6. Factor fully 27a3 - 64 [2 T]

7. The graph of has [3 T]

i) [1 T] a hole at:

ii) [1 T] a vertical asymptote:

iii) [0.5 T] as x → ∞ , y →

iv) [0.5 T] as x → -∞, y →

8. Determine the domain and range for the function [2 T]

D: _______________

R: _______________

9. Solve -5x ≤ 20 . [2 T]

10. Express in logarithmic form. [2 T]

11. Give the exact value for [1 A]

12. Given f(x) = -log2 (x - 4) +1 [total 4 A] State:

a.   the domain: [1 A]

b.   the equation of any vertical asymptote(s) [1 A]

c.   if the point P(x,-1) is on the graph off(x),  then x =      __________________________ [2 A]

13. Determine the exact value of [2 A]

14. The graph ofy = f(x) is given below. [total 5 K/U]

a. State a possible equation to describe the graph: [2 K/U] __________________________

b. The instantaneous rate of change at x=5 is: [1 K/U] __________________________

c. The average rate of change between  3 ≤ x ≤ 5 is: [2 K/U] __________________________

15. Write sin 450 cos150  - cos 450  sin150   as a single trigonometric function. [1 A]

16. Given f(x) = -x 2  and g(x) =  - 2x, write the expression of f( og )(x ). [2 A]

17. Given the graphs of two functions (below), where f is represented by the horizontal line and g is represented by the parabola, and units are 1: [total 4 A]

a. Sketch the graph of f - g on the same graph [2 A]

b. find (g 。f)(3) [2 A]

18. Determine the exact radian measure of 750 [1 A]

19. Solve for x, to two decimal places:  sin x = - 3/1 ≤ x ≤ 2π [2 T, 2 C] ___________________

20. If f(x) = x and g(x) = cos x , determine whether y = f (x)×g (x) is odd, even, or neither. [2 C]

21. When a biologist first counted, there were 1200 red ants in a particular colony. After 8 months, there were 5400 ants in the colony. What was the monthly rate of growth? [2 C]