Page1
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.
Page1
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