Math 1431
LAB session 8
Quiz 14
A)( 1, 2)
C)(2, 3)
B)( 1, 3) [ ( 1, 2)
D)( 2.1, 1)
Example 1:
Find the vertical and horizontal asymptotes of
A)( 1, 2)
C)(2, 3)
Example 2:
f (x) =
3x
6x 4
B)( 1, 3) [ ( 1, 2)
D)( 2.1, 1)
f (x) =
3x
6x 4
Find the vertical and horizontal asymptotes of f (x) = p
f (x) =
2x
x2 + 8
5 cos (x)
cos (x) 1
7
f (x) = p
Example 3:
f (x) =
Find the vertical and horizontal asymptotes of
A)( 1, 2)
C)(2, 3)
D)( 2.1, 1)
3x
6x 4
f (x) = p
A)( 1,#:
2)
Question
B)( 1,
2x
x2 + 8
5 cos (x)
cos (x) 1
3) [ ( 1, 2)
Find
the3)
horizontal
C)(2,
D)( asymptote
2.1, 1)
f (x) =
5x2
f (x) = 2
3x + 1
f (x) =
3
3x
sin (2x)
f (x) =
6x
1
4
7
2x
f (x) = p
x2 + 8
f (x) =
Question #:
5 cos (x)
cos (x) 1
B)( 1, 3) [ ( 1, 2)
f (x) =
5 cos (x)
cos (x) 1
5x2
f (x) = 2
3x + 1
Find the vertical asymptote f (x) =
3
sin (2x)
7
1
2x
x2 + 8
Example 4:
Determine whether or not the graph of
f (x) =
3
sin (2x)
f (x) = 5(x
7
1
3
6) /5 has a vertical tangent or vertical cusp at x=6.
Example 5:
Determine whether or not the graph of
f (x) = 5(x
f (x) = 4x /5
2
7
3
6) /5
3x /5 has a vertical tangent or vertical cusp at x=0.
1
f (x) = 4x /5
2
Example 6:
Determine whether or not the graph of
f (x) =
3x /5
p
4x 3 x
7
1
6
has a vertical tangent or vertical cusp at x=6
Question #:
f (x) =
p
4x 3 x
Determine whether or not the graph of f (x) = 3(x
7
6
4
5) /5 has a vertical tangent or vertical cusp at x=5
Example 7:
f (x) = 3(x
Give the full analysis for the following function f (x) = x
4
5) /5
f (x)
cos (2x) + 15
on [0, ⇡]
f
f (x) =
f (x) = 2
f (x) =
f
7
A)( 1, 15 )
B)( 15 , 1)
C)(
1
, 1)
5
D)( 25 , 1)
A)4
B)
5
16
C)
9
16
A)( 2.2, 0.6) [ (4.1, 1)
C)( 1, 2)
D)(2, 5.2)
D
B
Question #:
f (x) = x
cos (2x) + 15
Which of the following is true about the graph of f (x) = 12x2 +
27
+ 10 ?
x
7
Question #:
The graph of f′(x) is shown below. Which of the following is true about graph of f(x)?