1. In all the problems do the following:
Starter – Day November 5
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. 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?

6. 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?

7. Find all Complex Zeros: Three different ways