Algebra 2 Units 3-5 Flashcards

Mathematical Constants and Sequences

• e (Mathematical Constant): An irrational number approximately equal to 2.71828182845, important in finance and science as the base for exponential functions.
• Arithmetic Sequence: A sequence where each term is obtained by adding a constant value to the previous term.
• Geometric Sequence: A sequence where each term is found by multiplying the previous term by a constant factor.

Complex Numbers and Functions

• Complex Number: A number represented as a + bi, with a and b being real numbers, and i representing the square root of -1.
• Even Function: A function f where f(x) = f(-x) for all x; characterized by symmetry around the y-axis.
• Odd Function: A function f where f(x) = -f(-x) for all x; exhibits symmetry through a 180-degree rotation about the origin.

Polynomial and Rational Functions

• Degree of a Polynomial: The highest exponent of the variable x in a polynomial expression when arranged as a sum of terms.
• Polynomial Function: A function defined by a sum of terms where each term is a constant multiplied by a whole number power of x.
• Rational Function: A function defined as a fraction of polynomials, encompassing polynomials themselves as they can be written with a denominator of 1.

Properties of Functions

• End Behavior of a Function: Describes how function outputs behave as input values become increasingly large or small, approaching specific behavior at infinity.
• Horizontal Asymptote: The line y = c indicates that functions approach the value c as inputs grow large or small, affecting the graph's behavior at extremes.
• Vertical Asymptote: The line x = a indicates points where the function is undefined and where outputs tend towards infinity as they approach a from either side.

Logarithms and Logarithmic Functions

• Logarithm: The exponent needed for a given base (e.g., base 10) to yield a particular number; the natural logarithm is denoted as ln(x).
• Logarithmic Function: Defined as f(x) = k loga(x), grows slowly and does not approach a horizontal asymptote.

Miscellaneous Definitions

• Identity Equation: An equation that holds true for all possible values of the variables.
• Imaginary Number: A number expressed as bi, where b is real, and i is defined such that i^2 = -1.
• Multiplicity: Refers to the number of times a specific factor appears in the factored form of a polynomial.

Graphical Points and Sequences

• Relative Maximum: A point on a graph that is higher than all nearby points, showcasing a peak in the function's values.
• Relative Minimum: A point on a graph that is lower than surrounding points, indicating a trough in the function's values.
• Sequence: An ordered list of numbers that can theoretically extend indefinitely, such as the series of odd positive integers.
• Term of a Sequence: Any individual number within a sequence.

Test your understanding of key concepts in Algebra 2 with these flashcards covering Units 3 to 5. Each card provides definitions and explanations of important terms like the mathematical constant e, arithmetic sequences, and complex numbers. Perfect for quick revision and concept reinforcement.