Unit Five: Lesson 2: Graphs of Polynomial Functions
Part One: Odd Degree Polynomials
Below are some examples of polynomial functions....
Name
Linear
Quadratic
Cubic
Quartic
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Function
y  2x  1
f x   3x 2  6x  2
f x   x 3  x  1
y  x4  x3  x  3
Degree
One
Two
Three
Four
Even or Odd?
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Recall :
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 The DEGREE of the polynomial is the degree of the term with the highest exponent.
 The coefficient of the term with the highest exponent is called the LEADING COEFFICIENT.
example: f x   5x 3  7x 2  2x
5 is the leading coefficient.
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The degree is 3.
example: f x   2x  3x 4  5x 3
-3 is the leading coefficient
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The degree is 4.
Today we will look at those functions with odd degree.
yx
For example, the family of functions
y  x 3 and so on.
y  x5
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1
For each of the following cubic functions, use the graphing calculator to sketch a neat graph.
a) y  x 3  12x
e) y  x 3  3x 2  9x  3
b) y  3x 3  9x
f) y   x 3  9x 2  15x  9
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c) y  x 3  6x 2  16
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g) y  3x 3  9x 2  10
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d) y  3x 3  18x 2  27x  6
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h) y   x 3  3x 2  2
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Use the grids below. Put a maximumof two of the graphs on one grid. Be sure to label them.
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2
3
4
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Using the graphs you just completed, state the x-intercepts and the end behaviour in the table below.
Function
x-intercepts
a) y  x 3  12x
b) y  3x 3  9x
c) y  x 3  6x 2  16
d) y  3x 3  18x 2  27x  6
e) y  x 3  3x 2  9x  3
f) y   x 3  9x 2  15x  9
g) y  3x 3  9x 2  10
h) y   x 3  3x 2  2
End Behaviour on the
right as x  
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End Behaviour on the left
as x  
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Answer the following questions:
1. When the leading coefficient is negative, how does the graph change compared to when the leading
coefficient is positive?
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The next two questions require a review of quadrant numbers (see below).
2. When the leading coefficient is positive, the cubic graphs extend FROM quadrant number __________ to
quadrant number __________________.
3. When the leading coefficient is negative, the cubic graphs extend FROM quadrant number __________ to
quadrant number __________________.
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