Algebra 2
Name: ___________________
Directions: Simplify the following.
1) 6 x 5  3 x 5  x 0
2)
x 2 x 5
x4
3) x3  x 2 y
18x10
1
x7
14r 2 s 3t 4
4)
35r 2 s 5t 3
x5 y
 3 p 4 q 1 
5)  2 3 
 8p q 
2r 4 t
5s 8
2
64q 8
9 p12
6) For each of the following below, answer the following questions.
a. State whether the following are functions.
b. If it is a function, state the domain and range.
c. State whether or not the inverse is a function.
a. {(5, 8), (7,1), (9, 7), (11, 12), (13, 7)}
a. function
b. D:{5,7,9,11,13}
R{8,1,7,12}
c. Inverse not a function
b. {(-2,4), (0, 6), (-2, 8), (0,10), (-2, 12)}
a. not a function
b. inverse is a function
c.
d.
a. is a function
b. D: all reals, R: y>2
c. Inverse not a function
a. Function
b. D and R all reals
c. inverse is a function
Let f(x) = x – 3 and g(x) = x2 – 4x + 7. Write an expression for each function.
STATE ANY DOMAIN RESTRICTIONS!
7.
(f + g) (x)
x 2 - 3x + 4
10.
f g (5)
9
13.
x=10
f ( x)  7
g
8.  (x)
f
2
x - 4x + 7
;x ¹ 3
x-3
11.
f – g (x)
9. f g ( x)
x 2 - 4x + 4
12. g (-4)
-x 2 + 5x -10
39
14.
15. g (2 x )
36
f ( g (8))
4x 2 - 8x + 7
Write the letter that best answers the questions or completes the
statement.
____C_____ 16. The number 9.854 belongs to which set of numbers?
a. Integers
b. Whole Numbers
c. Rational Numbers
d. Irrational Numbers
___B____ 17. Which property of addition is illustrated by (a + b) + c = a + (b + c)
a. Commutative Property b. Associative Property
c. Identity Property
d. Inverse Property
___C______18. Which of the following is the range of the function y = x2 – 3?
a. x > -3
b. x < -3
c. y > -3
d. y < -3
___B_____ 19. What is the identity function?
a. y = 0
b. y = 1
b. x = y
d. y = x2
____________________________________________________________
20. Graph each function, and state the domain and range.
y = x2 + 4
D:all reals
R: y ³ 4
21. Graph a function with a domain of
3< x < 3 and a range of –5 < y< 5.
FIND THE INVERSE.
–
22.
1
f ( x)  x  4
3
f -1 ( x ) = 3x -12
23.
y
x 1
3
y-1 = 3x -1
Vocab Review:
24. What is the difference between discrete and continuous functions?
Continuous functions are all connected, discrete has parts that do not connect.
25. What does a one to one function mean?
Both a relation and its inverse are functions.
* Look over all of your notes for chapter 2. If you have questions, see me.