Algebra 2 EOC Flashcards

Key Algebra 2 Concepts

• Relation: Refers to a set of ordered pairs, linking elements from one set to another.

• Domain: The set of all x-coordinates (inputs) in a relation or function.

• Range: The set of all y-coordinates (outputs) in a relation or function.

• Function: A specific type of relation where each x-coordinate is unique; passes the vertical line test.

Variation Types

• Direct Variation: Expressed mathematically as ( Y = kx ), where ( k ) is a non-zero constant.

• Inverse Variation: Represented by ( Y = \frac{k}{x} ), indicating that y varies inversely with x.

• Joint Variation: A scenario where y varies jointly with multiple variables, such as ( x ) and ( z ).

Asymptotes in Rational Functions

• Horizontal Asymptote: Indicates that a rational expression has no horizontal asymptote when its degree is higher in the numerator than the denominator.

• Vertical Asymptote: Found by setting the denominator equal to zero and factoring.

Rational Expressions

• X-Intercepts for Rational Expressions: These can be determined by dividing out any common denominators.

Factoring Techniques

• Sum or Difference of Cubes: Factorable using the formula ( a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2) ).

Advanced Formulas

• Continuous Compounding: Described by the formula ( A = Pe^{(rt)} ), where ( A ) is the amount, ( P ) is the principal, ( r ) is the rate, and ( t ) is time.

• Compound Interest Formula: Given by ( A = P(1+\frac{r}{n})^{(nt)} ), where ( n ) is the number of times interest is compounded per year.

Complex Numbers

• Square Root of -1: Denoted as ( i ), the imaginary unit.

• Definition of ( i^2 ): By definition, ( i^2 = -1 ).

Exponents and Inverses

• Rational Exponent Meaning: Represents "power over root", indicating the relationship between exponents and roots.

• Finding Inverse of a Function: To find the inverse, switch ( x ) and ( y ) in the equation and solve for ( y ).

Solving Equations

• Absolute Value Equations: Solved by setting the expression inside the absolute value equal to both the positive and negative constants.

Systems of Equations

• Methods to Solve Systems: Include graphing, substitution, combinations, and elimination methods.

Quadratic Function Form

• Standard Form for Quadratic: The equation format is ( f(x) = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants.