Polynomial Functions
How do you find the number of turning points?
Subtract on from the degree
Name the 3 types of Asymptotes.
Vertical, Horizontal, Oblique(Slant)
Why do we use test points?
To see where to shade or to see if it is true or false
If f(2) is equal to zero, what is 2 called?
A factor
If a+bi is a zero then...
What does the end behavior tell you about the polynomial?
How the graph looks at the end
When the degree is at the top is smaller than the degree at the bottom, what is the asymptote.
y=0
When solving inequalities, one side must always be..
Zero
If f(9)=16, what is the 16 called?
The remainder
Find the remaining zeros: Degree 6; Zeros: 3, 3+i, -2-i, 0
3-i, -2+i
If the multiplicity is odd, then the graph does what?
Crosses the x-axis
Find the asymptotes of the following function R(x)=(x^2-4)/(x-2)
None
Which value must be excluded from the solution of a rational inequality?
Any number that makes the denominator undefined
Use the Remainder Theorem to find the remainder of the following polynomial: f(x)=x^4+8x^3+12x^2; x+1
R=5
Find the remaining zeros: Degree 5; Zeros: 2, -5i, i
5i, -i
What is another name for x intercepts?
Zeros
A rational function can have both vertical and horizontal asymptotes.
True or Yes
Solve the following: x^2−9>0
(-inf,-3)U((3, inf)
List the potential zeros of the polynomial function: f(x)=-2x^3+4x^2-2x+8
+/-1, +/-1/2, +/-2, +/-4, +/-8
Find all of the zeros of the function: x^3-x^2+16x-16
4i, -4i, 1
Find the polynomial with the following characteristics: Zeros 0 multiplicity 4, 2 multiplicity 3, -1 multiplicity 2; Degree 9
f(x)=x^4(x-2)^3(x+1)^2
Below:(-1,0); Above: (-inf, -1) and (1, inf)
Solve (x+2)/(x-3)>0
(−∞,−2)∪(3,∞)
Use the Rational Zeros Theorem to find all the zeros of the polynomial function. f(x)=x^4+15x^2-16
-1, 1
Use the given zero to find the remaining zeros: x^4-21x^2-100; Zero: 2i
2i, -5, 5