Polynomial Functions

1
Section 5.2

• Polynomial Functions Models

2
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.

3
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

4
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.

5
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

6
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

7
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

8
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

9
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

10
Graphically Evaluate f(-2)
We want the value for y when x -2 f(-2) 4
11
Graphically Evaluate f(-3)
f(1) ?
f(0) ?
We want the value for y when x -3 f(-3) 0
12
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
13
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.

14
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.
15
Homework Sec. 5.2

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