MCV 4U1/a
NAME:____________
/20 KU
/2 COMM
/8 APP
1.
__
QUIZ: Unit 4 - Curve Sketching
For the function
f ( x) 
x2  x  6
,
x 1
a)
Determine the equation of any vertical asymptotes and the behaviours around the vertical
asymptotes.
b)
Determine the equation of any horizontal or oblique asymptotes and state the behaviours
around the asymptote. Draw a sketch of the behaviours around the horizontal and/or oblique
asymptote(s). Show all work!
[3K]
[5K]
4
2
-4
-2
2
4
-2
-4
2.
f is a differentiable function with second derivative, f x   x 2  1 2 x  1 . State all of the
2
function’s critical numbers. Then state the intervals of concavity and determine the x-coordinate(s)
of any point(s) of inflection. Show all work!
[6K]
3.
For the function
f ( x) 
x
, state all of the functions critical numbers and determine if each
x 1
2
one corresponds to a local maximum, local minimum, or neither. Show all work!
[4K]
3x 2
For the function f ( x) 
, determine the equation of its horizontal asymptote (using
6x 2  2x  5
4.
methods from this class) and its end behaviours in proper mathematical form. Show all work!
[2K+2C]
Y




Sketch the graph of a function with the following
properties:
There are relative extrema at (-1, 7) and (3, 2)
There is a point of inflection at (1, 4)
The graph is concave down only when x  1
The x -intercept is -4 and the y -intercept is 6
6
4
2
X
5.
8
[4A]
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
6.
f (x) , of a
function f (x ) . On which intervals is the graph of f (x ) :
The following represents the second derivative graph,
4
2
a) concave up
b) concave down
-4
-2
2
-2
-4
c) make a possible sketch of
f (x) , assuming that f (0)  2
4
2
[4A]
-4
-2
2
-2
-4
4
4