Quiz 10 Solution Fall 2010 September 29
These problems are from Lesson 5 material.
Find a polynomial p that has the given zeros (roots) and multiplicity.
1.
Zero (Root)
Multiplicity
3
2
4
1
In order for 3 to be a zero (root) of multiplicity 2, ( x + 3 ) 2
Quiz 13 Solution Fall 2010 October 6
This problem is from Lesson 7 material.
Find the zeros (roots) of f ( x ) = 3 x 5 23 x 4 + 34 x 3 + 38 x 2 64 x 24 .
Also, give a factorization for the polynomial.
Factors of 24 : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24
Factor
Quiz 14 Solution Fall 2010 October 8
These problems are from Lesson 7 material.
Given g ( x ) = 3 x 4 7 x 3 10 x + 24
1.
List all the possible rational zeros (roots).
(4 pts.)
Factors of 24: 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24
Factors of 3: 1, 3
Possible rati
Quiz 8 Solution Fall 2010 September 22
These problems are from Lesson 4 material.
Without finding the inverse function, state the domain and range of both the
function and its inverse. The sketch of the graph of the function might be
helpful. (9 pts.)
1.
Quiz 1 Solution Fall 2010 August 30
The following problem is from Lesson 1.
3x + 5
0 . (9 pts.)
2x
Solve the nonlinear inequality
NOTE: This is a two part problem. One part of the problem is to solve the
nonlinear inequality
equation
3x + 5
> 0 . The oth
Quiz 5 Solution Fall 2010 September 13
These problems are from Lesson 3.
Sketch the graph of the following functions. Use the sketch to state the range of the
function.
1.
f (x) =
3x 2
(4 pts.)
Setting f ( x ) = y , we have that y =
3x 2 y + 2 =
3x .
y
Quiz 12 Solution Fall 2010 October 4
These problems are from Lesson 6 material.
Use synthetic division to do the following.
1.
If f ( x ) = x 5 4 x 4 + 16 x 2 + 4 x 16 , then find f ( 2 ) .
5
4
2
4
16
Coefficients of x x + x + 4 x 16
1 4
0
16
4 16
2
1
12
Quiz 2 Solution Fall 2010 September 1
The following problems are from Lesson 2.
Find the domain of the following functions.
1.
g( x ) =
5x 2
9 x2
(4 pts.)
Want (Need): 9 x 2 0
9 x 2 0 ( 3 + x ) ( 3 x ) 0 3 + x 0 and 3 x 0 x 3 and
x3
Thus, the domain of th
Quiz 11 Solution Fall 2010 October 1
These problems are from Lesson 6 material.
Find the following. Identify the quotient and remainder functions. You can
use synthetic division when it would apply.
1.
( 2 x 4 11 x 3 + 22 x 2 23 x + 15 ) ( x 2 3 x + 2 )
2
Quiz 3 Solution Fall 2010 September 3
The following problems are from Lesson 2.
1.
If f ( x ) = 3 x 2 8 x , then find f ( x + h ) . (3 pts.)
f ( x + h ) = 3( x + h )2 8 ( x + h ) = 3( x 2 + 2 x h + h 2 ) 8 x 8 h =
3 x 2 + 6 x h + 3h 2 8 x 8 h
2.
If g ( x
Quiz 6 Solution Fall 2010 September 17
These problems are from Lesson 4 material.
Given the function h, find functions f and g such that h = f g . (9 pts.)
1.
h( t ) =
3
27 t 3
Let f ( t ) =
2.
h( x ) =
3
t and g ( t ) = 27 t 3
5
3 ( 4 x + 7) 2
Let f ( x
Quiz 7 Solution Fall 2010 September 20
This problem is from Lesson 4 material.
Find the inverse function for g ( x ) = 4 ( x 2 ) 2 + 5 , x 2 . (9 pts.)
Let y = 4 ( x 2 ) 2 + 5 . Solving for x, y = 4 ( x 2 ) 2 + 5
y 5 = 4( x 2) 2 ( x 2) 2 =
y5
x2=
4
Sinc
Quiz 15 Solution Fall 2010 October 13
These problems are from Lesson 9 material.
Sketch the graph of the following functions. State the range of the function.
1.
f ( x ) = 6e x
(4 pts.)
Range = ( , 0 )
2.
5
g( x ) =
2
x4
3
(5 pts.)
Range = ( 3 , )
Quiz 9 Solution Fall 2010 September 24
This problem is from Lesson 5 material.
Find the zeros (roots) and their multiplicities. Discuss the implication of the
multiplicity on the graph of the polynomial. Determine the sign of the infinity
that the polynom