2415 Pre-Calculus
Mid-Term Review#1
1) Given 4
2 x

1 
8
3 x

2
, determine x.
Name:
4
2 x

1 
8
3 x

2
 
2 x

1 
 
3 x

2
4 x 2 9 x

6 x
 
8
5
2) Evaluate the difference quotient
  h
   
, h

0 when h
  h
    h
  h
  x
 h

3 
3
 x
 h


1
3 0 
3
2 1 
3
1 2 
1
0 3 x h x h x h x h

3 x

3 h
   x
3 
3 x .
  h
   

3 x
2 
3 xh
 h
2 h
3) Find the vertical asymptotes of

2
&
5 x
 
1
4) Find the horizontal asymptote of

3 x
4 
2 x

4
5 x 2 
3 x

2

2
&
5 x
 
1

7 x 2 
2 x

4
2 x
2 
3 x

2 y
7
3
1
2 2

3.5
5) Find the equation for the slant asymptote of

15 x
3 
2 x
2 
5 x

1
3 x
2  
1
LongDivison : y

5 x

1

2415 Pre-Calculus
Mid-Term Review#1
Name:
6) If
 x
2 
4 x

12
2 x 2 
3 x

2
, the location of the hole is

,

 x
2
2 x 2


4 x
3 x


12
2



2 x x


6
1



 x x


2
2

 x
 
2 f
 
2

2 6
 

8
5 therefore hole :


2,
8
5 
7) Write the function for the graph to the right. x

1, x

1, x
 
2 y
  x

1
 x

1
 x

2
 y
 x
3 
3 x

2
8) Find the domain of

25
 x
2
.
25
 x
2 
0 x
 
5 then plot on the number line

5,5

9) Solve the following rational inequality.
5 x

1 x

5

1
5 x

1 x

5
5 x

1 x

5

1
1 0
5 x 1 x

5
4 x

6

0 x

5
5

0 where x
 
5 and x
2

5,
3
2


   


 y





    x

2415 Pre-Calculus
Mid-Term Review#1
Name:
10) Solve the following polynomial inequality
 x

2
  x

3
  x

2
 
0 x

2, x

3, x
 
2

Plot on the line and test inequality

, 2
    
11) If 7 2 i is a root of a polynomial function having real coefficients, then what must be another root of the same function? f
  i
   
2 i
    i
  x
2 
1 4 x

53
12) Solve the following equation x
4 x
2
2 
9
 x
2 x

3
 x
3

3
 x

3
 x

3



4 x
2 x
2

9

2 x
2 
3 x
 
0

2 x

3
 x

3
 
0
2 x x

3
 x
3

3

 x

3

2
3 can't be an answer b/c DR.
 
3
13) The graph to the right is
Increasing:

, 3
  
Decreasing:
 
3, 2
  
Constant:

4,
 
14) Given
   x
2 x 1 and a)
 f
 g
 
  x

( x
2  
1)
4
 
3 2 x , find: b)
  
 
3 2 x
  x 2  
1

 
2 x
3 
5 x
2  
3

2415 Pre-Calculus
Mid-Term Review#1 c)
 g f
 
 x
  x
 
1

4 x 2 
10 x

5
Name: d) f

1 x y x y x y

1
3 2 y
 x


2
3
 x
2
3

3
2
3

0
15) Write 3 functions that have the same
 y transformations as the graph to the right. y

2
 x

2

2 
1 y

2 x y
 x
2

2

1
      







 
16) Determine algebraically if the following functions are even or odd, then state any symmetry. a)
   x
4  x
2 
1 f
  x
4 x
2
1 even c)

5
 x
2 b)
  
4 x
5 
3 x
3  
1 f
 
4 x
5 
3 x
3 x 1 neither d)
 x
4 
2 x
3  x f
 
5
 x
2  even f
  x
4 
 
2
 even x 3 x odd
 odd
17) What is the sum of the roots of the polynomial function?
  
2 x
4 
5 x
3 
11 x
2 
20 x

12
Use remainder theorem then Syntheic Div: x
 
3, 2, 2,
1
2 x

2415 Pre-Calculus
Mid-Term Review#1
Name:
18) Provide a list of the possible rational roots from the given function
  
24 x
4 
32 x
3 
21 x
2 x 6 p
 q
1, 2, 3, 6,
1
,

3
,

1
2 2 3
....

1
24
19) Find a polynomial function having integral values with roots of 2, -3 and 2i. x

2, x
 
3, x

2 i
   x

2
 x

3
  x

2 i
 x

2 i


 x
2  
6
  x
2 
4

 x 4 
..... 24

turns out 4th degree polynomial with 3 zeros.
x

2 x

3 x

2 x

1
 
5
 
3
 
2
 
1
 
5
.