1. In all the problems do the following:
Starter – Day November 4
Content Objective: We will work with and analyze complex zeros. *Complex numbers have real parts and imaginary parts.
In all the problems do the following:
Find the zeros (you might have to factor first)
List the multiplicity of each zero
Does the graph touch or cross at each zero
Describe left/right end behavior
Find a power function that is an end behavior asymptote
Sketch the graph.
Zero
Multiplicity
Touch/Cross?
Left End Behavior
Right End Behavior
Power Function E.B.A.
X intercept(s)
Y intercept

2. LAB Writing
Explain in writing what the y-intercept and x-intercepts of a graph are.

3. Complex Zeros: Conjugate Pairs
3i, -3i 2+5i, 2-5i 9i 3, 1-7i

4. Complex Zeros: How many real roots?
Total # of Zeros
Possible # Real
Possible # Imaginary
Total # of Zeros
Possible # Real
Possible # Imaginary
Total # of Zeros
Possible # Real
Possible # Imaginary

5. Rational Roots Constant Factors Leading Coefficient Factors
Possible Rational Roots
Constant Factors
Leading Coefficient Factors
Possible Rational Roots
Constant Factors
Leading Coefficient Factors
Possible Rational Roots

6. Descarte’s Rule of Sign
# positive real zeros:
# negative real zeros:
# positive real zeros:
# negative real zeros:
# positive real zeros:
# negative real zeros:

7. Intermediate Value Theorem
If there is a polynomial with points (2,1) and (4, -3), is there at least one zero between x=2 and x=4?
If f(x) is a polynomial function with f(2)=1 and f(4)= -3, is there at least one zero of f(x) between x=2 and x=4?

8. Intermediate Value Theorem
If f(x) is a polynomial function with f(-6)=7 and f(-1)= 1, would it be safe to say that f(x) must be equal to 4 somewhere between -6 and -1?
If f(x) is a polynomial function with f(-4)=5 and f(1)= -4, is there at least one zero of f(x) between x=-4 and x=1?

9. Remainder Theorem If , what is the remainder when you divide by ?
What is the value of ?

10. Find all Complex Zeros: Three different ways