Download REV 4B

College Algebra
REVIEW 4B
RATIONAL ZERO THEOREM
1. List all the possible rational zeros of the function f(x) = 8x5 – 3x3 + 6
2. How many zeros does the function f(x) = -4x7 + 3x5 + 5x3 – 9 have?
3. Simplify: 3x3 + 4x2 – x + 5 ÷ x – 2
4. Use the Remainder Theorem to find f(-2) given f(x) = 3x3 + 5x2 – 7x – 6
5. Given -2/3 is a zero of (x) = 12x2 – x – 6 find all the remaining roots.
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College Algebra
REVIEW 4B
FINDING ZEROS
Find all the zeros (real and imaginary) of the given polynomial functions.
6. f(x) = 2x3 + 7x2 + 2x – 3
7. h(x) = x4 + x2 – 12
8. g(x) = x3 – 8x2 + 13x
9. h(x) = 2x2 + 6x + 5
10. f(x) = x4 – x3 – 2x – 4
College Algebra
REVIEW 4B
WRITING EQUATIONS
Find the equation of a polynomial function that has the given zeros.
11.
-4, 0, 3
12.
-1, ±6
13.
3, ±4i
14.
-2, 0, ±5i
15.
4, 2 ± 3i
College Algebra
REVIEW 4B
DISTRIBUTIVE PRACTICE
16. Given f(x) = 3√3x + 2, find f-1(x) using algebra.
17. Sketch the graph of x2 + y2 – 6x – 8y + 16 = 0
18. Given f(x) = x2 + 2x and g(x) = x2 + x + 4, find f(g(-2)).
19. Graph the following:
f(x) =
x+1
x < -2
x2
-2 < x < 2
-2x + 5 x > 2
20. Sketch each graph:
a) y = |x – 3|
b) y = x2 + 5
c) y = x3 – 2
d) y = -√x + 2