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Section 5.2

- Polynomial Functions Models

Polynomial Functions

- Linear Function f(x) -5x 1
- Quadratic Fcn f(x) 3x2 5x 1
- Cubic Fcn f(x) x3 4x2 3x -2
- Whats the difference?
- A linear fcn is a first degree fcn.
- A quadratic fcn is a 2nd degree fcn.
- A cubic fcn is a 3rd degree fcn.

Polynomial Functions

- Polynomial functions must have non-negative

integer exponents. - Determine whether f(x) represents a polynomial

function. - f(x) 5x3 x - 10
- f(x) 3x-2 - 5x
- f(x) x-2.5 1
- f(x) x1/2

Evaluate a polynomial function

- Numerically
- (table)
- Graphically
- Find y for the given value of x
- Symbolically
- Plug the given value of x into the fcn.

Symbolically Evaluate f(2) for f(x) x2 5x

4

- We want to find the value of y when x 2
- y f(2) (2)2 - 5(2) 4
- 4 - 10 4
- -2
- For f(x) x2 - 5x 4, f(2) -2

Symbolically Evaluate f(x) -3x4 2 for x 2

- We want to find the value of y when x 2
- y f(2) -3(2)4 - 2
- -3(16) -2
- -50
- For f(x) -3x4 2 , f(2) -50

Evaluate f(x) -2x3 - 4x2 5 for x -3

- We want to find the value of y when x -3
- Y f(-3) -2(-3)3 - 4(-3)2 5
- 23

Numerically Evaluate f(2) for f(x) x2 5x

4

- We want to find the value of y when x 2
- Make an input-output table in your TI-83 Y1

x2 - 5x 4

- Find where x 2 and read the value for y .
- For f(x) x2 - 5x 4, f(2) -2

Numerically Evaluate f(-3) for f(x) x2 5x

4

- We want to find the value of y when x -3
- Make an input-output table in your TI-83 Y1

x2 - 5x 4

- Find where x -3 and read the value for y .
- For f(x) x2 - 5x 4, f(-3) 28

Graphically Evaluate f(-2)

We want the value for y when x -2 f(-2) 4

Graphically Evaluate f(-3)

f(1) ?

f(0) ?

We want the value for y when x -3 f(-3) 0

HW, 40 (p. 294)

- The polynomial function
- f(x) -0.064x3 0.56x2 2.9x 61
- models the ocean temperature in degrees F at

Naples, FL. (x1 corresponds to January, x2 to

February, etc. - What is the average ocean temperature in April?

f(4) -0.064(4)3 0.56(4)2 2.9(4) 61 ? 77.5o

HW, 40

- The polynomial function
- f(x) -0.064x3 0.56x2 2.9x 61
- models the ocean temperature in degrees F at

Naples, FL. (x1 corresponds to January, x2 to

February, etc. - Make a table of f, starting at x 1, and

incrementng by 1. During what month is the avg.

temp. the least.

HW, 40

- The polynomial function
- f(x) -0.064x3 0.56x2 2.9x 61
- models the ocean temperature in degrees F at

Naples, FL. (x1 corresponds to January, x2 to

February, etc. - Graph f in 1, 12, 1 by 50, 90, 10. Estimate

when the maximum ocean temperature occurs, What

is this temperature.

In TI-83, calculate the maximum.

Homework Sec. 5.2

- 1-5 7-12 15-19 odds 23-26 31-35 odds 41-44.

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