1. Make sure you have book and working calculator EVERY day!!!
Polynomial Functions
2.1 (M3)

2. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
Yes it’s a Polynomial.
It is in standard form.
Degree 4 – Quartic Trinomial
Its leading coefficient is 1.
a. h (x) = x4 – x2 + 3 1 4
b. Yes it’s a Polynomial.
Standard form is
Degree 2 – Quadratic Trinomial
Leading Coefficient is

3. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
c f (x) = 5x2 + 3x –1 – x
c. Not a polynomial function
d. k (x) = x + 2x – 0.6x5
d. Not a polynomial function
e. f (x) = 13 – 2x
e. polynomial function;
f (x) = –2x + 13;
degree 1
linear binomial,
leading coefficient: –2

4. Graph Trend based on Degree
Even degree - end behavior going the same direction
Odd degree – end behavior (tails) going in opposite directions
Leading Coefficient
Leading Coefficient

5. Symmetry: Even/Odd/Neither
First look at degree
Even if it is symmetric respect to y-axis
When you substitute -1 in for x, all signs stay the SAME
Odd if it is symmetric with respect to the origin
When you substitute -1 in for x, all of the signs CHANGE
Neither if it is NOT symmetric around the
y-axis or origin

6. Tell whether it is even/odd/neither
f(x)= x2 + 2
f(x)= x2 - 4x
f(x)= x3
f(x)= x3 + x
f(x)= x3 + 5x +1

7. Additional Vocabulary to Review
End Behavior:
Left side x– ∞, f(x) ____
Right side x+∞, f(x) ____

8. Additional Vocabulary to Review
Domain: set of all possible x values
Range: set of all possible y values
Symmetry: even (across y), odd (around origin), or neither
Interval of increase (where graph goes up to the right)
Interval of decrease (where the graph goes down to the right)
End Behavior:
Left side x– ∞, f(x) ____
Right side x+∞, f(x) ____

9. Polynomial Functions and Their Graphs
There are several different elements to examine on the graphs of polynomial functions:
Local minima and maxima:

10. Give the Local Maxima and Minima
Must use y to describe High and Low
On the graph above: A local maximum: f(x) = A local minimum: f(x) =

11. Finding a local max and/or local min is EASY with the calculator!
Graph each of the following and find all local maxima or minima:
Now describe their end behavior.

12. Describe the Interval of Increasing and Decreasing
Must use x to describe Left to Right
(Left to Right)
The graph is: y x
Increasing when ___________
Decreasing when _____________
Increasing when ___________

13. Assignment Page 69 #1-3 Classify #8-10 End Behavior
#11-13 Symmetry (Even/Odd/Neither)
#14-16 Max/Min, Domain/Range, Intervals of
Increasing and Decreasing