Name Algebra 2 review for cumulative exam
Review Packet #2, page 1

REVIEW PACKET #2 for Cumulative Exam April 2014

NO CALCULATORS ON THIS REVIEW PACKET

x / f(x)
1 / 16
2 / 9
3 / 0

9. Let . The table at the right shows some of thefunction’s values.

a.Using information from the table, identify one of the factors of f(x).

b.Factor f(x) completely.

c.Sketch the graph of f(x). Your graph must have accurately drawn x- and y-intercepts
and the correct overall shape.

10.Sketch the graphs for each of the following equations. Work neatly and use a ruler.

a.
b. /
/

11. is a linear function. Suppose and . Write a formula for . Use point-slope form.

12.Write the function formula equation for each polynomial function described and graphed below. [Note about the graphs: the graphing windows vary, and the x- and y-axes might be scaled differently. You should use the graph only to get an idea of the graph’s shape.]

a. / The function below is quadratic (degree 2).
Its x-intercepts are and , and its vertex is .
/ b. / The function below is cubic (degree 3). Its x-intercepts are , , and. Its graph goes through the point .

c. / The function below is cubic (degree 3).
Its xintercepts are and , and its yintercept is .
/ d. / The function below is linear (degree 1).
Its slope is and its graph goes through the point .

13. Find these function values.

a.For f(x) = , find f().b. For f(x) = 2 log (x - 3) + 7, find f(10003).

14. Find a function formula for the inverse function f–1(x). Show your work.

a.b.

15. Let and let .

a. Find

b. Find

c. Find

16. A golf ball is hit into the air. Its height, after x seconds, is given by the function .

a.What is the ball’s height after 3 seconds?

b.When does the ball land?

c.How high does the ball go?

d.Sketch the graph of . Include the coordinates of any important points.

e. What is the domain? (In other words, what x values make sense as inputs in this problem situation?)
17.Solve these equations. Go as far as possible without a calculator.

a.b.

c. d.

e. f.

18. The graph of a function f(x) is shown on the grid. Each grid square is a 1-by-1 square.

Answer these questions. You do not have to show work. You may need to make decimal estimates ofnumbers that fall between whole numbers.

a.Find f(3).

b.Solve f(x) = 3.

c.Find the zeros of f(x).

d.Solve f(x) = -8.

e. What is the maximum point of f(x)?

f.What is the domain of f(x)?

g. What is the range of f(x)?

19. Sketch a graph of the following functions. Include the coordinates of the zero(s), vertex, and y-intercept on your graph.

a.

zero(s):

vertex:

y-intercept:

b.

zero(s):

vertex:

y-intercept:

c.

zero(s):

vertex:

y-intercept:

d.

zeros(s)

vertex:

y-intercept:

20. Find the zero(s) for the following functions. If there are no zeros, state “no zeros”.

a. b.

c. d.

e.

Name Algebra 2 review for cumulative exam
Review Packet #2, page 1

ANSWERS

  1. is a factor
  2. Vertical line at x=-3

.

  1. or
  2. or
  1. f(10003) = 15
  2. 4 seconds
  3. Find the vertex: (2, 64). The max. height is 64 feet.
  4. 0 x 4
  1. x = 0 , x = 3/5
  2. x = 0,
  3. x = 6
  4. x = 1
  5. f(3) = 1.3
  6. x = 1, x = 2
  7. x = 4, x 3.8
  8. No solution
  9. (1, 5)
  10. -5 x 6
  11. -4 y 5
  12. Check graphs on your calculator:
  13. Zeros: 2, 2; vertex: (0, 4); y-intercept: (0, 4)
  14. Zeros: 0, 5; vertex: (2.5, 12.5); y-intercept: (0, 0)
  15. Zeros: 10, 2; vertex: (4, 36), y-intercept: (0, 20)
  16. Zeros: 1, 7; vertex: (3, 16); y-intercept: (0, 7)
  1. x = 2
  2. x = 2
  3. x = 15