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Polynomial Functions

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Polynomial Functions

Lesson 9.2

- Definition:
- The sum of one or more power function
- Each power is a non negative integer

- General formula
- a0, a1, … ,an are constant coefficients
- n is the degree of the polynomial
- Standard form is for descending powers of x
- anxn is said to be the “leading term”

- Consider what happens when x gets very large negative or positive
- Called “end behavior”
- Also “long-run” behavior

- Basically the leading term anxn takes over
- Comparef(x) = x3 with g(x) = x3 + x2
- Look at tables
- Use standard zoom, then zoom out

- Compare tables for low, high values

The leading term x3 takes over

For 0 < x < 500the graphs are essentially the same

- Compare graphs ( -10 < x < 10)

- We seek values of x for which p(x) = 0
- Consider
- What is the end behavior?
- What is q(0) = ?
- How does this tell us that we can expect at least two roots?

- Graph and ask for x-axis intercepts
- Use solve(y1(x)=0,x)
- Use zeros(y1(x))
- When complex roots exist, use cSolve() or cZeros()

- Giveny = (x + 4)(2x – 3)(5 – x)
- What is the degree?
- How many terms does it have?
- What is the long run behavior?

- f(x) = x3 +x + 1 is invertible (has an inverse)
- How can you tell?
- Find f(0.5) and f -1(0.5)

- Lesson 9.2
- Page 400
- Exercises 1 – 29 odd