End Behaviors

Domain - x values
Range - y values

domain → +∞, range → +∞ (means it rises on the right)

domain → -∞, range → -∞ (means it falls on the left)

• domain → -∞, range → +∞ (means it rises on the left)
• domain → +∞, range → -∞ (means it falls on the right)

• domain → +∞, range → -∞ (falls on the right)
• domain → -∞, range → -∞ (falls on the left)

Degree
0- constant
1-linear
2-quadratic
3-cubic
4-quantic
5-quintic

Terms
monomial
binomial
trinomial
quadrinomial
polynomial

Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• 3 examples
• a² - 9 (a+3) (a-3)
• b² - 4 (b+2) (b-2)
• c² - 1 (c+1) (c-1)

• Trinomial perfect squares
  • a² + 2ab + b² = (a + b)(a + b) or (a + b)²
    • 3 examples
    • a² + 4a + 2 (a+2)²
    • a² + 6a +9 (a+3)²
    • x² + 8x + 16 (x+4)²
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• 3 examples
• x² - 8x + 16 (x-4)²
• a² - 4a + 2 (a-2)²
• a² - 6a +9 (a-3)²
• Difference of two cubes
• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• 3 examples
• x³-27= (x-3)(x²+3x+9)
• a³-125= (a-5)(a²+5a+25)
• d³-1= (d-1)(d²+d+1)

• Sum of two cubes
• • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
      • x³+27= (x+3)(x²-3x+9)
      • a³+125= (a+5)(a²-5a+25)
      • d³+1= (d+1)(d²-d+1)
• Binomial expansion
  • (a + b)³ = Use the pattern  a³+3a²b+3ab²+b³
  • (a + b)⁴ = Use the pattern  a⁴+4a³b+6a²b²+4ab³+b⁴

Circles and more

• If a=c, then the equation is a circle.                          3x²+3x²=36

                                              

• If a does not equals c, and thay are the same signs then the equation is an elipse.     2x²+x²=25

• If a or c = 0 then the equation its a parabola.                            y²-2x=5

• If a or c are different signs, the equation is a hyperbola.           2x²-2x²=24

Dimensions of a Matrix

The Dimensions of matrices basically are te rows and the colums thet the Matrices have.
The rule for this to work properly is to multiply the column times the row.

Ex. Here is a 4x2 and a 2x3 matrices.

To multiply this kind of matrices you have to multiply the number of columns in matrix A times the number of rows in matrix B to finally get the answer if 4x3.

Regularlly you'll get the number of rows of the first matrix and the number of columns in the second matix. 

How to Multiply Matrices?

Here we have an example of a 3x2 multiplied by a 2x4.

to do this you have to multiply every number by its following number in the second matrix. The rows of A times the coloumns of B. 



Kinds of Systems

Inconsistent Systems: They have no solutions and never intersept. They are parallel.
Dependent Consistent System: They are equations with the same slope and the same y-intercept. one line in top of the other.
Independent Consistem System: This kind of system only has one solution. (intercept only once)

Consistent Independent:

Dependent Consistent:

Inconsistent System: