4.
Vertical asymptotes at x= -3 and
6
=
x
5.
x-intercepts: (-5, 0) and (4, 0);
y-intercept:
(0,
9
10
)
6.
Looking at the equation it is not clear whether the function has any
local maxima or minima.
7.
As
±
∞
→
x
, the function
acts like
2
2
x
x
y
=
and its graph
approaches the line y= 1.
Horizontal asymptote: y = 1.
Here is how the function looks on
the graph.

MHF 4U Unit 7: RATIONAL FUNCTIONS
17
Curve Sketching
Here is a check-list of the things to consider when you make a sketch of
the graph
( )
x
f
y
=
.
1.
Factor the numerator and denominator (into linear factors if
possible). Simplify.
2.
Find the domain of
( )
x
f
.
3.
Determine where the function is negative and where positive.
4.
Find the points of discontinuity and their types – vertical
asymptotes or donut holes.
5.
Find the x- and y-intercepts.
6.
Find the local maxima and local minima of the function.
(Later you will learn how to do this. For now use your graphing
calculator.)
7.
Determine the end behaviour of the function and see
whether the function has any horizontal or oblique
asymptotes.
8.
Examine the symmetry of the curve with respect to the y-axis
and with respect to the origin, i.e. whether the function is
even or odd.
pg. 272 # 1, 2
pg. 273 # 5
pg. 274 # 9, 14
Assignment C: GRAPHS OF RATIONAL FUNCTIONS

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- Spring '19