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Name ______Date ______Pd ______

Review #13–Polynomial Functions

# 1 – 4 Sketch the graph of each polynomial (no y-scale) using the

roots of the function.

1. f(x) = x2(x − 3)32. f(x) = (x + 1)(x – 3)2

3. f(x) = −x3 + 25x4. f(x) = 4x4 – 17x2 + 4

5. Determine algebraically if the functions in #3 and #4 are even, odd, or neither.

a) f(x) = −x3 + 25x b) f(x) = 4x4 – 17x2 + 4

6. I’m a quartic with a double root at -1 and a root at 2 and a root at 3. (1, 24) is a point on me. Write my function in factored form and sketchme.

7. Write the equation in polynomial form.

Use transformations of f(x) = x3 and f(x) = x4 to graph each function.

8. f(x) = 1 − (x − 5)3 9. f(x) = x4 − 5

Domain:______Range: ______Domain:______Range: ______
Use long division to determine that the given polynomial is a factor of f(x). Use the result to write f(x) in completely factored form.

10. f(x) = x3 + x +2, (x + 1)11. f(x) = x5 + x3 – x2 – 1, (x2 + 1)

12. Sketch a complete graph and label the maximums and minimums.

Answer the questions about f(x).

f(x) = –2x3– 4x2 + 10x + 30

a)

Applications – Review all of the types of volume problems.

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Answers to Review #13

1.

2.

3.

4.

5. a) f(-x) = -f(x) ODD

b) f(x) = f(-x) EVEN

6. f(x) = 3(x + 1)2(x – 2)(x – 3)

7. f(x) = -2x3 + 2x2 +16x – 24

8. 9.

10. f(x) = (x + 1)2(x – 2)

11. f(x) = (x2 + 1)(x – 1)(x2 + x + 1)

12. a)

Min (-2.120, 9.879)

Max (.786, 34.418)

b) (2.473, 0) (0, 30)

c) (-2.120, .786)

(-, -2.120),(.786, )

d) -30

e) 2.407

f) (2.473, )

g) (-, 2.473]

h) 30

i) No

j) No