Functions
What must c equal to make the set of points a function?
(1, 2) (3,5) (5,8) (1, c)
c = 2
factor x2 + 2x + 1
(x+1)(x+1) or (x+1)2
Solve for x
| 4 - 8x | = 20
x = -2
x = 3
Put the following polynomial into standard form
x3 - 5x4 + 2x - 3x2
-5x4 + x3 - 3x2 + 2x
What do we call the highest power on x?
Degree
What test do we use to see if a graph represents a function?
The Vertical Line Test
What is the min/max point of a quadratic function called?
The Vertex
Solve the system
y = -3x -5
y = -6x - 11
(-2, 1)
What is your remainder when you divide a polynomial by one of its factors?
Zero
What is the end behavior if the lead coefficient is positive and the degree is odd?
Down/Up
Find f(2)
-3
Find the vertex of the following function
x2 + 4x - 5
(-2, 11)
Solve the system
x - y = -5
x - 5y = -29
(1, 6)
Divide using long division
x4 + 2x2 + 1 divided by x2 + 3
x2 - 1 + 4 / (x2 + 3)
Find the end behavior of the following polynomial.
x3 + 5x6 - 3x5
up/up
f(x) = -x2 and g(x) = 6x + 2
find f x g (2)
-56
Factor the following function
f(x) = 3x2 +13x - 10
(3x - 2)(x + 5)
Solve using a matrix
-3x - 4y + 2z = 22
2x + 4y - 4z = -8
4x - 4y + 4z = -16
(-4, -5, -5)
Divide using synthetic division
2x4 - 5x3 - 14x2 + 47x - 30 divided by x - 2
2x3 - x2 - 16x + 15
Give the zeros and their multiplicities of the following polynomial
x(x -2)(x - 2)(x + 1)(x + 1)(x + 1)(x - 5)4
-1 3
0 1
2 2
5 4
f(x) = 2x2 and g(x) = 3x - 5
find f(g(3))
32
Find the zeros of the following function
f(x) = (x - 3)2 - 1
x = 2
x = 4
Solve for y, fully simplify
3x - 6y < 12
y > 1/2x - 2
Fully factor the following polynomial using the given factor.
x3 - 3x2 - 28x + 60 given (x - 2) is a factor
(x - 2)(x + 5)(x - 6)
Sketch a graph of the following polynomial.
-2(x - 1)(x + 2)2(x - 3)
end behavior down/down
zeros | multiplicity
-2 2
1 1
3 1