The document discusses polynomial functions of the form f(x) = anxn + ... + a1x + a0. It provides information to identify properties of a polynomial function based on its graph, including whether the highest term's exponent n is odd or even, the sign of the leading coefficient an, the lowest possible value of n, and the number of real zeros. It also gives rules for the behavior of graphs based on the sign of an and whether n is odd or even. The document concludes by listing the information needed to graph polynomial functions and providing two examples of functions to graph.

1. Polynomial Functions
PSHS Main Campus
July 9, 2012
PSHS Main Campus () Polynomial Functions July 9, 2012 1/4

2. Polynomial Functions
f (x) = an xn + ... + a1 x + a0
Given the graph on the right,
identify:
1 If n is odd or even.
2 The sign of an .
3 The lowest possible value of n.
4 The number of real zeroes of
the function.
PSHS Main Campus () Polynomial Functions July 9, 2012 2/4

3. Polynomial Functions
f (x) = an xn + ... + a1 x + a0
Given the graph on the right,
identify:
1 If n is odd or even.
2 The sign of an .
3 The lowest possible value of n.
4 The number of real zeroes of
the function.
PSHS Main Campus () Polynomial Functions July 9, 2012 2/4

4. Polynomial Functions
f (x) = an xn + ... + a1 x + a0
Given the graph on the right,
identify:
1 If n is odd or even.
2 The sign of an .
3 The lowest possible value of n.
4 The number of real zeroes of
the function.
PSHS Main Campus () Polynomial Functions July 9, 2012 2/4

5. Polynomial Functions
f (x) = an xn + ... + a1 x + a0
Given the graph on the right,
identify:
1 If n is odd or even.
2 The sign of an .
3 The lowest possible value of n.
4 The number of real zeroes of
the function.
PSHS Main Campus () Polynomial Functions July 9, 2012 2/4

6. Polynomial Functions
f (x) = an xn + ... + a1 x + a0
Given the graph on the right,
identify:
1 If n is odd or even.
2 The sign of an .
3 The lowest possible value of n.
4 The number of real zeroes of
the function.
PSHS Main Campus () Polynomial Functions July 9, 2012 2/4

7. Polynomial Functions
Properties of Graphs
an n Description
(+) even comes down from left, goes up to the right
(+) odd up from left, up to right
(−) even up from left, down to right
(−) odd down from left, down to right
Maximum number of turning points = n − 1
PSHS Main Campus () Polynomial Functions July 9, 2012 3/4

8. Graphing Polynomial Functions
Information needed to graph Polynomial Functions
1 Identify behavior at left and right sides of the graph.
2 Identify zeros of the graph.
3 Identify y-intercept.
Graph the following:
1 f (x) = (x2 − 1)(x + 2)
2 g(x) = (2 − x)(x − 3)(x + 1)(x − 1)
PSHS Main Campus () Polynomial Functions July 9, 2012 4/4