MAT 150 College Algebra NAME:_________________
Fall 2015 Quiz #8
1.
The graph of f x
 x
4 
2 x
3 
13 x
2 
4 x

28 is shown to the right. Use the graph to help you find ALL the zeroes of f(x).
25
20 y
15
10
5
-5 -4 -3 -2 -1
-5
-10
-15
-20
-25
2.
Find a polynomial function (in equation form) that would “fit” ALL of the following conditions. You can leave the function in factored form as well.
7
6
5 y
1 2 3 4 5
-7 -6 -5 -4 -3 -2 -1
4
3
2
1
1 2 3 4 5 6 7
-1
-2
-3
-4
-5
3. Graph the rational function on the grid provided. Clearly label any asymptotes, intercepts, holes, etc. y f ( x )

3 x x


1
6
5
4
3
2
7
6
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
1 2 3 4 5 6 7
-3
-4
-5
-6
-7 x x x

4. Graph the rational function on the grid provided. Clearly label any asymptotes, intercepts, holes, etc. y
7
6 f ( x )
 x
2 x
2

 x
4

6
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6 7
-2
-3
-4
-5
-6
-7
5. A graph of rational function is shown below. Find a rational function that fits the given picture. Make sure your rational function matches the x-intercept(s).
4 y
2 x
-5 -4 -3 -2 -1
-2
-4
1 2 3 4 5
6.
A graph of f ( x ) is shown to the right. Use the graph shown to help you determine the intervals where ( )

0
7
6
5
2
1
4
3
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
7.
Solve the following inequality. Put your answers in interval notation.
y
1 2 3 4 5 6 7
 x

3
 x

4

2 
0 x x

8.
Solve the following inequality. Put your answers in interval notation.
x x

1

2

0
9. FOUR functions are defined below. Use them to answer the questions that follow.
f ( x )
 x
2 
2 g(x)
3
5
4 y
h(x)
2
-5 -4 -3 -2 -1
1
1 2 3 4 5 x t ( x )
 x

6
-1
-2
A)
 f  g

(

3 )
-3
-4
-5
B) ( 9 )
C)
 g  h

( 0 ) D)
 t  f

( x )
10.
Find two functions, f ( x ) and g ( x ) , such that
 f  g

( x ) form the function: y
 x

1
2 x y
0 -4
3 -1
5 0
7 1
9 10
11 20

11. Do the following:
A) Find
 g  f

( x ) given that f ( x )

3
2 x

1 g ( x )

2 x
3

2
B) Based off of your work in PART A), are the functions inverses? Why or why not?
12.
THREE different one-to-one functions are given below. Find f

1
( x ) for each. f ( x )
 x
3
4 y
 f ( x ) 7 f ( x )
6
5
4
3
2
1 x x y
-4 9
-3 8
-2 7
-1 6
-7 -6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6 7
-2
-3
-4
-5
-6
-7
13. Graph the following function. Clearly identify the BASIC function, Clearly label at least
ONE point and clearly label any horizontal of vertical asymptotes.
g ( x )

2
 x 
4
7
6 y
5
4
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1 2 3 4 5 6 7 x

14. Solve the following exponential equations:
A) 3
2 x

5 
1
9
.
EXTRA CREDIT –

1
1. If f ( x )
 x
and g x

3

3 x x


1
, find
1
B) e x
2  e x

2
 f  g

( x ) , simplify your answer.
2. Solve: x
5

3
 x
3

1

MAT 150 College Algebra NAME:_________________
Fall 2015 Quiz #8 Calculator Part.
1.
Given the function: f ( x )

1
7
 x
4 
2 x
3
Calculator Type:_________

13 x
2 
4 x

28

, do the following:
A) Use your calculator to graph the function . Show me your input and a sketch of what you see on your calculator including the picture window you used
B) Use your calculator to help you find the x-intercept(s).
C) Determine the interval(s) ( )

0 .
2.
Use your calculator to help you solve the inequality shown below.
Show me your input and a sketch of what you see on your calculator including the picture window you used, final answer should be in interval notation. x
2 
2 x

4

3.
Given the rational function, h ( x )

3

10 x x
2 
4
, do the following items:
A) Use your calculator to graph the function . Show me your input and a sketch of what you see on your calculator including the picture window you used
B) Use your calculator to help you find the find LOCAL EXTREMA of the function.
C) Determine the interval(s) where the function is increasing.
4.
Use your calculator to graph the function . g ( x )

 x

2

2
1
 x 2

3 x x

 
1

1
Show me your input and a sketch of what you see on your calculator including your picture window you used, make sure you include open or closed dots where needed.