Untitled Quiz

Functions

• A function pairs each element of the domain (input/x) with one element of the range (output/y).
• Functions can be represented using verbal descriptions, tables, graphs, or equations.

Variables

• Independent Variable: The input or x-value of a function.
• Dependent Variable: The output or y-value that relies on the input.

Function Characteristics

• Domain: All possible input values (x) for a function.
• Range: All possible output values (y) for a function.

Evaluation and Notation

• Evaluate: Process to find the output value for a specified input.
• Function Notation: Written as f(x) instead of y, representing functions in a concise manner.

Parts of an Equation

• Variable: A symbol (typically a letter) representing a number.
• Coefficient: A number multiplied by a variable.
• Constant: A number that remains unchanged.
• Operator: Symbol indicating mathematical operations (addition, subtraction, etc.).
• Exponent (Power): Indicates how many times a base is multiplied by itself.

Types of Functions

• Parent Function: The simplest form of a function from which other functions are derived.
• Constant Function: Maintains the same output regardless of input; represented as a horizontal line.
• Linear Function: Relationship where input equals output; represented as y = x.
• Quadratic Function: Involves the square of the input; produces a U-shaped graph known as a parabola (y = x²).
• Cubic Function: Involves the cube of the input.
• Square Root Function: Derives output from the square root of the input, undefined for negative values.
• Absolute Value Function: Measures distance from zero; graph appears as a V shape (y = |x|).
• Exponential Function: Base raised to a variable power, with the input as the exponent.
• Rational Function: Involves fractions; undefined for an input of zero (cannot divide by zero).

Graphing Concepts

• Graph: A representation of ordered pairs (input/output values) forming a line or curve on the coordinate plane.
• Ordered Pair: A duo of numbers that identifies a point on the coordinate plane.
• Coordinate Plane: Divided into four quadrants by the x-axis (horizontal) and y-axis (vertical).

Data Types

• Discrete Data: Can only take specific values; for example, counting items like the number of students.
• Continuous Data: Can take any value within a range; for example, heights of individuals.

Transformations

• Alterations to a parent graph include:
  • Reflection: Flips the graph across a line.
  • Dilation: Changes the size of the graph, either enlarging or shrinking.
  • Horizontal Shift: Moves the graph left or right.
  • Vertical Shift: Moves the graph up or down.