Polynomial Functions Worksheet
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1
2Mathematics 30-2
Name: ______________________________
5.1 Exploring the Graphs of Polynomial Functions
Date: ______________________________
New Vocabulary
Scatterplot: A set of points on a grid, used to visualize a relationship or possible trend in data.
Polynomial Function: A function that contains only the operations of multiplication and addition with
real-number coefficients, whole-number exponents, and two variables.
y 5x
3x 7, y
4x 8, f x
x
3x 4
For example:
3
2
Degree: The highest exponent in a polynomial function.
For example: The degree of
y
4x
3
8x
2
5
is ‘3’.
Leading Coefficient: The coefficient of the term with the greatest degree in the polynomial function
in standard form.
f x
5x
2
8x 7
For example: The leading coefficient in the function
is ‘-5’.
Constant Term: The term in the polynomial function that has no variable, i.e. the degree is ‘0’.
y
4x
6x
7x 1
For example: The constant term in the function
3
2
is ‘1’.
Linear Function
Quadratic Function
Cubic Function
A polynomial function of
A polynomial function of
A polynomial function of
first degree,
second degree,
third degree,
whose greatest exponent is
whose greatest exponent is ‘2’.
whose greatest exponent is ‘3’.
‘1’.
Standard Form is
Standard Form is
Standard Form is
f x
ax b, where a
0
f x
ax
2
bx c, where a
0
f x
ax
3
bx
2
cx d, where a
0
.
.
.
Examples:
Examples:
Examples:
2
1
3
y
2x 3, f x
x 4
y
x
2
3x 4, f x
x
2
4x 5
y
x
3
3x 2, f x
2x
3
4x
2
3
2
4
End Behaviour: The behaviour of the y-values of the function as x becomes very large.
Turning Point: Any point where the graph of a function changes from increasing to decreasing or
decreasing to increasing.
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