Algebra 2 Functions Flashcards

Function Types and Characteristics

• Absolute Value Function: Contains an algebraic expression enclosed within absolute value symbols, yielding non-negative outputs.
• End Behavior: Refers to the trends of a function's graph as the input variable (x) approaches positive or negative infinity.
• Extrema: Represents the highest (maximum) and lowest (minimum) values that a function can achieve, crucial in optimization.
• One-to-One Function: A function where each input (domain) corresponds to precisely one unique output (range), ensuring no repeated outputs.
• Onto Function: Implies that every output in the range has a corresponding input in the domain, covering all possible outputs.
• Piecewise-Linear Function: Composed of various linear equations defined over different intervals, creating distinct pieces on its graph.
• Step Function: Features a graph that resembles a series of connected line segments, resembling a staircase.
• Vertical Line Test: A method to determine if a relation is a function; if a vertical line intersects the graph at most once, it qualifies as a function.

Function Zeroes and Types

• Zero of a Function: Identifies the input value (x) that results in an output of zero from the function (f(x)=0).
• Not a Function: Describes a situation where the output directly inverses the input, breaking the definition of a function.
• Quadratic Function: Expressed in the form f(x) = ax² + bx + c, characterized by a parabolic graph, with 'a' being non-zero.
• Cubic Function: Defined by the equation f(x) = x³, featuring a graph that can exhibit one or two turning points and can extend to positive or negative infinity.
• Rational Function: Composed of two parabolas and asymptotes, which are lines that the graph approaches but never touches.
• Exponential Function: Characterized by the equation y = ab^x, where 'a' is a non-zero constant and 'b' is the base of the exponential function.
• Logarithmic Function: Described as f(x) = log_b(x) where base 'b' is positive and not equal to one; serves as the inverse to the exponential function f(x) = b^x.
• Square Root Function: Expressed as f(x) = √x, with a domain of [0, ∞) and range of [0, ∞), displaying a gradually increasing curve starting from the origin.