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