Algebra 2 Functions Flashcards

Functions Overview

• A function is a relation with unique outputs for each input; it pairs every domain element with a single range element.

Key Components of Functions

• Domain refers to the set of all possible input values of a function.
• Range consists of all possible output values that result from the function.

Types of Functions

• Parent Function: The simplest function in a family that serves as a reference for other functions.
• Linear Function: Characterized by a straight line, defined by the equation ( y = mx + b ), where ( m ) is the slope.
• Quadratic Function: A polynomial function of degree 2, typically represented as ( y = ax^2 + bx + c ).
• Absolute Value Function: Described by ( y = |x| ); contains all non-negative outputs for real numbers.
• Square Root Function: Given by ( y = \sqrt{x} ), outputs non-negative values for non-negative inputs.
• Cubic Function: A polynomial of degree 3, expressed as ( y = ax^3 + bx^2 + cx + d ).
• Cube Root Function: Defined by ( y = \sqrt[3]{x} ), allowing both negative and positive outputs.
• Rational Function: Expressed as the ratio of two polynomials, can have points of discontinuity.
• Exponential Function: Written as ( y = a(b^x) ); typically shows rapid growth or decay.
• Logarithmic Function: The inverse of the exponential function, generally noted as ( y = \log_b(x) ).

Transformations of Parent Functions

• Transformations modify parent functions to derive other functions in the same family.
• Translation: Involves shifting a parent function vertically or horizontally.
• Reflection: A flip over the line ( y = x ); alters the orientation of the graph.
• Dilation: Creates a stretch or compression, changing the rate of growth or decline of the function.

Special Features in Function Behavior

• Inverse of a Function: The reflective counterpart across the line ( y = x ). Found by swapping ( x ) and ( y ) in the original equation.
• Point Discontinuity: Represents locations where the function is not defined, leading to gaps in the curve.
• Asymptote: A line that a function’s graph approaches closely but never intersects, indicating limits in function behavior.

Test your understanding of functions with these flashcards! This quiz covers essential concepts such as function definitions, domain, range, and parent functions. Enhance your algebra skills and prepare for advanced topics in mathematics.