Unit 4 Polynomial Functions
4.1 Graphing Polynomial Functions
What are some common characteristics of the graphs of cubic and quartic polynomial functions?
Vocab:
Monomial: a number, a variable, or the product of a number and one or more variables with whole number
exponents.
Polynomial: a monomial or a sum of monomials.
Polynomial function in standard form:
Where:
an ≠ 0,
exponents are all whole numbers,
coefficients are all real numbers
Examples of Polynomial Functions:
Decide whether or not each function is a polynomial function, is it in standard form? Rewrite in in standard form if it is not.
End Behavior of Polynomial Functions:
Even Degree Odd Degree
Ex: y=x2 or y=-x2 Ex: y=x3 or y=-x3
Graph the following Polynomial Function:
Graph the following Polynomial Function:
Is it a polynomial function?
Type?
Is it in standard form? (rewrite if not)
Degree?
# solutions/roots?
y-intercept?
Odd or even degree?
Leading coefficient?
End behavior?
Is it a polynomial function?
Type?
Is it in standard form? (rewrite if not)
Degree?
# solutions/roots?
y-intercept?
Odd or even degree?
Leading coefficient?
End behavior?
Given
Is it a polynomial function?�Type?�Is it in standard form? (rewrite if not)�Degree?�Number of real zeros/roots?�y-intercept?�Odd or even degree?�Leading coefficient?�End behavior? �
Given
Is it a polynomial function?�Type?�Is it in standard form? (rewrite if not)�Degree?�Number of real zeros/roots?�y-intercept?�Odd or even degree?�Leading coefficient?�End behavior? �
Given
Is it a polynomial function?�Type?�Is it in standard form? (rewrite if not)�Degree?�Number of real zeros/roots?�y-intercept?�Odd or even degree?�Leading coefficient?�End behavior? �
Given the following graph of a polynomial function tell me what you can find out about the leading coefficient and the degree.
Given the following graph of a polynomial function tell me what you can find out about the leading coefficient and the degree
Exit Ticket:
Sketch a graph with the following characteristics:
Sketch a graph of the polynomial function f having these characteristics.
• f is increasing when x < 0 and x > 4.
• f is decreasing when 0 < x < 4.
• f(x) > 0 when −2 < x < 3 and x > 5.
• f(x) < 0 when x < −2 and 3 < x < 5.
Use the graph to describe the degree and leading coefficient of f.
Sketch a graph with the following characteristics:
Sketch a graph of the polynomial function f having these characteristics
.
• f is increasing when x < 0 and x > 4.
• f is decreasing when 0 < x < 4.
• f(x) > 0 when −2 < x < 3 and x > 5.
• f(x) < 0 when x < −2 and 3 < x < 5.
Use the graph to describe the degree and leading coefficient of f.