Algebra Class: Functions and Their Properties

Parent Function

• Simplest function of a family; serves as a template for other functions.
• For quadratic functions, the parent function is ( y = x^2 ).
• Graph of ( y = x^2 ) is a parabola.

Exponential Function

• Form where the value is a constant raised to the power of the argument.

Linear Function

• A function whose solutions graph as a straight line.

Quadratic Function

• Defined by the standard form ( f(x) = ax^2 + bx + c ) with ( a \neq 0 ).
• The graph forms a parabola, which can open upwards or downwards.

Absolute Value Function

• Contains an algebraic expression in absolute value symbols.
• Graph features a vertex and a line of symmetry.

Rational Function

• Features two graphs (parabolas) and asymptotes, which are lines the graph approaches but never touches.

X-Intercept

• The point at which a graph crosses the x-axis.

Y-Intercept

• The point at which a graph crosses the y-axis.

Increasing Function

• A function where output values grow larger over a given interval.

Decreasing Function

• A function where output values diminish when viewed from left to right along the graph.

Minimum

• The smallest value of a function, known as a local minimum or global minimum depending on the range.

Equation

• A mathematical statement asserting the equality of two expressions, indicated by an equals sign.

Domain

• Set of all possible values of the independent variable (x-values) that produce real y-values.

Range

• Differences between the highest and lowest values in a distribution.

Input

• Elements inserted into a system for a specific outcome.

Output

• The results produced by a system's operations.

Asymptote

• A line that a graph approaches indefinitely without intersecting.

Opens Upward

• A characteristic of a parabola with a minimum point.

Opens Downward

• A characteristic of a parabola with a maximum point.

Infinity

• Refers to endless or limitless aspects relating to space, time, or distance.

Expression

• A combination of numbers, variables, and operations without an equals sign.

Polynomial

• An algebraic expression involving variables and coefficients, featuring addition, subtraction, multiplication, and non-negative integer exponents.

Even Function

• A function whose graph is symmetric about the y-axis, satisfies ( f(x) = f(-x) ).

Odd Function

• A function whose graph is symmetric about the origin, satisfies ( f(-x) = -f(x) ).

Point of Intersection

• A location where two graphs meet or share common coordinates.

Endpoints

• Term for the terminal points on the ends of line segments.