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What is the general rule of a function?
If the X that you try only has one Y that’s a function
function
A relation that assigns one value of the dependent variable to each value of the independent variable. A function is always a relation.
Relation
A relation may produce more than one output for a given input. A relation may or may not be a function.
Y axis (or values)
Dependent variables/ Outputs/ Vertical Axis
X values (Or X Axis)
Independent variables/Input/ Horizontal Axis
Vertical Line Test
if a vertical line passes through a graph of an equation more than once, the graph is not a graph of a function
Polynomial
Monomial or the sum of two or more monomials whose exponents are positive
Example (5a²+ba-3)
Monomial
A polynomial with only one term; a number, variable, or the product of a number and one or more variables
example(4a²b)
Binomial
Algebraic Expression consisting of two terms( Example: 5a+6)
Trinomial
A polynomial with exactly three terms (Example: a²+2a-3)
Like terms
Must have exactly the same base and the same exponent (may have different coefficients)
Coefficient
Number being multiplied by the variable
Base
Number being multiplied by itself
Exponent
How many times that base is multiplying itself
like terms in the same expression can be
Combined by adding their coefficients
Multiplying Polynomials
Multiply each term in the first polynomial by each term in the second polynomial, then combine like terms
How to use complete the square
For completing the square rmb
Add (b/2)² to both sides
Factor using (X+b/2)²
Key Note:
NEVER FORGET TO SINPLIFY RADICALS
Factoring the difference between perfect squares
(a+b)² = (a+b)(a-b)
Factoring the sun and difference of perfect squares
a³+b³ = (a + b) (a²-ab+b²)
a³-b³ = (a-b) (a²+ab+b²)
Factoring trinomials
Use X and Square method
Irrational numbers
decimal that does not terminate, square roots
Rational numbers
Decimal terminates and repeats
Zero
Solution or root of an expression
Graph of X>1
not included (increasing) and not shaded circle
Graph of X < 1
Not included/ not shaded / decreasing
X > 1
Included/increasing /shaded
x < 1
Included/ shaded/ decreasing
ANYTHING GREATER/ LESS THAN OR EQUAL TOO IS SHADED THEREFORE IT IS
INCLUDED
ANYTHING GREATER/ LESS THAN IS not SHADED SO IT IS
Not included
Rule for solving inequalities
If an inequality is multiplied or divided by any NEGATIVE number the direction of the inequality sign changed.
Unidentified slope
Vertical
Zero slope
Horizontal
Positive slope
right to left
Negative slope
Left to right
R
Correlation coefficient
r
linear/ nonlinear fit of the data
Note
Whatever you divide by include in the paranthesis
Other note
Whenever simplifying literal math expressions always factor out the common term
