9 week test review problems Problems like 1-11 are definitely on the test 1. Write an equation for the linear function f satisfying the given conditions. Then graph it. f(2) = 8 and f(-2) = 12 2.Find the vertex & axis of symmetry: f(x) = -3(x + 8) Find the vertex, axis of symmetry, and rewrite in vertex form: f(x) = 2x 2 – 8x – 5

4. Write the equation in vertex form given the vertex & a point vertex: (-1, 4), point: (2, -2) 5. Use vertical free-fall motion a ball is thrown from 10 feet with an initial velocity of 100 ft/sec. a. What is the maximum height of the ball? b. what is the height of the ball after 4 seconds?

6. Analyze the function f(x) = 5 x 2 find the power and constant of variation determine the domain, range, continuous/discontinuous, increasing/decreasing intervals, even/odd, boundedness, local extrema (max/min), asymptotes, end behavior

7. Sketch the graph by hand: f(x) = 4(x – 1) 2 (x + 5) 3 (x – 3) 1 st determine: highest degree, end behavior, the zeros & what the graph does at each 0 8. Find the 0’s algebraically or graphically f(x) = 5x 3 – 5x 2 – 10x

9. Find the cubic function given the zeros 1, -2, use long division to divide f(x) = x 3 – 3x + 4, d(x) = x use synthetic division to divide f(x) = 2x 3 – 3x 2 + 4x – 7, d(x) =x-2

12. Solve the quadratic equation a. by factoring: 2x 2 + 5x – 12 = 0 b. by quadratic formula: 4x x + 23 = Perform operations with complex numbers: a. (2 – 3i) + (6 + 5i) b. (7 – 3i) – (6 – i) c. (7i – 3)(2 + 6i) d i 1 – 4i

14. Anything with the 12 basic functions: look at Ch 1 test for possible questions, except for # Finding inverses a. f(x) = x b. f(x) =

16. Building functions given f(x) = x – 5 and g(x) = 2x + 8 find: f(x) + g(x) a. f(x) – g(x) b. f(x)g(x) c. f(x) g(x) d. f(g(x)) e. g(f(x))

17.Describe the transformation a. f(x) = 3(x – 2) b. f(x) = - sin x – 4 c. f(x) = -1/2ln(x + 2) d. f(x) = |x| + 4

Answers Please only check after you’ve done the problems 1.y = -x Vertex: (-8, 10), axis of symmetry: x=-8 3.Vertex: (2, -13), axis of symmetry: x = -13, f(x) = 2(x – 2) 2 – 13 4.f(x) = -2/3(x + 1) 2 – 4 5.a. -16t t + 10, maximum height: 166 ¼ ft b. 154 ft

Answers cont’d 6. power: -2, constant of variation: 5, domain: (-∞,0)U(0,∞), range:(0, ∞), infinite discontinuity, even, boundedness: none, local extrema: none, asymptotes: VA:x=0, HA: y=0, end behavior: 0, 0

Answers cont’d 7. Highest degree: 4x 6 end behavior: up, up 0’s: 1: tangent, -5: wiggles, 3: cross

Answers cont’d 8. 0, -1, 2 9. (x-1)(x+2)(x+3) = x 3 + 4x 2 + x – x 2 – 2x x x 2 + x x – 2 12a. {-4, 3/2} b.

Answers cont’d 13a i b. 1 – 2i c. -48 – 4i d i 17 15a. f -1 (x) = b. f -1 (x) = x 2 + 4

Answers cont’d 16a. 3x + 3 b. –x + 3 c. 2x 2 – 2x – 40 d. x – 5 2x +8 e. 2x + 3 f. 2x – a. right 2, up 8, stretch of 3 b. down 4, reflection c. left 2, reflection, compression of ½ d. up 4