9 week test review problems

Problems like 1-11 are definitely on the test1. 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)2 + 10 

3. Find the vertex, axis of symmetry, and rewrite in vertex form:f(x) = 2x2 – 8x – 5

4. Write the equation in vertex form given the vertex & a pointvertex: (-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 functionf(x) = 5

x2 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)1st determine: highest degree, end behavior, the zeros & what the graph does at each 0

8. Find the 0’s algebraically or graphicallyf(x) = 5x3 – 5x2 – 10x

9. Find the cubic function given the zeros1, -2, -3

10. use long division to dividef(x) = x3 – 3x + 4, d(x) = x + 2

11. use synthetic division to dividef(x) = 2x3 – 3x2 + 4x – 7, d(x) =x-2

12. Solve the quadratic equation a. by factoring: 2x2 + 5x – 12 = 0b. by quadratic formula: 4x2 + 20x + 23 = 0

13. Perform operations with complex numbers:a. (2 – 3i) + (6 + 5i)b. (7 – 3i) – (6 – i)c. (7i – 3)(2 + 6i)d. 2 + 3i 1 – 4i

14. Anything with the 12 basic functions:look at Ch 1 test for possible questions, except for #18

15. Finding inversesa. f(x) = x2 + 8b. f(x) =

16. Building functionsgiven f(x) = x – 5 and g(x) = 2x + 8find: 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 transformationa. f(x) = 3(x – 2)2 + 8b. f(x) = - sin x – 4c. f(x) = -1/2ln(x + 2)d. f(x) = |x| + 4

Answers

• Please only check after you’ve done the problems

1. y = -x + 102. Vertex: (-8, 10), axis of symmetry: x=-83. Vertex: (2, -13), axis of symmetry: x = -13,

f(x) = 2(x – 2)2 – 134. f(x) = -2/3(x + 1)2 – 45. a. -16t2 + 100t + 10, maximum height:

166 ¼ ftb. 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: 4x6 end behavior: up, up

0’s: 1: tangent, -5: wiggles, 3: cross

Answers cont’d

8. 0, -1, 29. (x-1)(x+2)(x+3) = x3 + 4x2 + x – 610. x2 – 2x + 1 + 2

x + 2 11. 2x2 + x + 6 + 5 x – 212a. {-4, 3/2}

b.

Answers cont’d

13a. 8 + 2i b. 1 – 2i c. -48 – 4i d. -10 + 11i 1715a. f-1(x) = b. f-1(x) = x2 + 4

Answers cont’d

16a. 3x + 3 b. –x + 3

c. 2x2 – 2x – 40 d. x – 5 2x +8

e. 2x + 3 f. 2x – 217. a. right 2, up 8, stretch of 3

b. down 4, reflection c. left 2, reflection, compression of ½

d. up 4