Algebra 2 Functions Flashcards

Study Notes

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

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 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.

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.