1. Polynomial Functions and Models
4.2
Understand the graphs of polynomial functions.
Evaluate and graph piecewise-defined functions
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2. Graphs of Polynomial Functions
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3. Constant Polynomial Function
Has no x-intercepts or turning points
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4. Linear Polynomial Function
Degree 1 and one x-intercept and no turning points.
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5. Quadratic Polynomial Functions
Degree 2, parabola that opens up or down. Can have zero, one or two x-intercepts. Has exactly one turning point, which is also the vertex.
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6. Cubic Polynomial Functions
Degree 3, can have zero or two turning points.
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7. Quartic Polynomial Functions
Degree 4, can have up to four x-intercepts and three turning points.
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8. Quintic Polynomial Functions
Degree 5, may have up to five x-intercepts and four turning points.
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9. Degree, x-intercepts, and turning points
The graph of a polynomial function of degree n  1 has at most n x-intercepts and at most n  1 turning points.
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10. Example Use the graph of the polynomial function shown.
a) How many turning points and x-intercepts are there?
b) Is the leading coefficient a positive or negative? Is the degree odd or even?
c) Determine the minimum degree of f.
Solution
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11. Group Work
Graph f(x) = 2x3  5x2  5x + 7, and then complete the following.
a) Identify the x-intercepts.
b) Approximate the coordinates of any turning points to the nearest hundredth.
c) Use the turning points to approximate any local extrema.
Solution
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12. Example Let f(x) = 3x4 + 5x3  2x2.
a) Give the degree and leading coefficient.
b) State the end behavior of the graph of f.
Solution
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13. Piecewise-Defined Polynomial Functions
Example Evaluate f(x) at 6, 0, and 4.
Solution
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14. Example Complete the following. a) Sketch the graph of f.
b) Determine if f is continuous on its domain.
c) Evaluate f(1).
Solution
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15. Copyright © 2006 Pearson Education, Inc
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley