5.2
Polynomial Functions & Graphs
Homework: Every Other Odd 29-69, All 71-75
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Examples of polynomial functions:
Polynomials DO NOT contain:
Denominators that include a variable.
Terms that have absolute-value.
Examples that are NOT polynomials:
The leading term of a
polynomial is the term with the highest exponent. Polynomials are
usually written in descending order
(from highest exponent to lowest exponent).
Like terms are terms with the same
variable raised to the same power.
If an expression contains like terms, the like terms are combined to
simplify the expression.
Example:
Examples of polynomial functions:
Example:
Example: The distance S(t), in feet, traveled by a body falling freely from rest in t seconds is approximated by the function:
A stone is dropped from a cliff and takes 8 seconds to hit the ground.
Approximate how high is the cliff?
Graphs of polynomial Functions:
The graph of a polynomial function is “smooth” – there are no sharp corners.
The graph of a polynomial function is continuous – there are no holes or breaks.
The domain of a polynomial function, unless otherwise indicated, is all real numbers.
Examples of graphs of polynomial functions:
The pattern that we observe about the range of each graph is that:
The range of a polynomial function of odd degree (highest power is an odd number)
is all real numbers.
The range of a polynomial function of even degree (highest power is an even number) is
Example:
