Functions and Relations Quiz

Functions and Relations

• A set is a collection of unique objects.
• An element is an object in a set.
• A relation associates elements in one set with elements of another.
• A way to represent a set is listing its elements within curly brackets { }.
• The set of first elements in a relation is called the domain, representing input values.
• The set of related second elements in a relation is called the range, representing output values.
• Functions are a special type of relation where each element in the domain is associated with exactly one element in the range.
• A graph represents a function when no two points lie on the same vertical line.
• Function notation, d(t), defines a function named d.
• Input is independent, expressed by x or t.
• Output is dependent, expressed by y or d.
• A linear equation is expressed as y = mx + b, where m is the rate of change (slope), and b is the y-intercept.

Domain and Range

• The domain of a function is the set of all possible input values (x-values).
• The range of a function is the set of all possible output values (y-values), often listed in order.
• Discrete graphs have unconnected points, while continuous graphs are unbroken.
• To describe the domain and range, use inequalities or interval notation.

Holes in the Graph

• A hole in a graph indicates a point where the function does not exist.
• The domain and range may be limited by holes.
• The domain and range are described using inequalities or interval notation (e.g., (-∞, 3) U (3, ∞)).

Vertical Line Test

• A graph represents a function if any vertical line drawn on the graph intersects the graph at most once.

Lines and Graphing

• The general equation of a line is y = mx + b, where:
  • y represents the dependent variable (output).
  • x represents the independent variable (input).
  • m represents the rate of change (slope).
  • b represents the y-intercept (the value of y when x = 0).

Midpoint

• The midpoint between two points (x₁, y₁) and (x₂, y₂) is calculated by averaging the x- coordinates and the y-coordinates:
  • Midpoint = ((x₁ + x₂)/2), ((y₁ + y₂)/2)).

Distance Between Two Points

• The distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula:
  • Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

Slopes of Parallel and Perpendicular Lines

• Parallel lines have the same slope.
• Perpendicular lines have negative reciprocal slopes (the product of their slopes is -1).

Test your understanding of sets, relations, and functions with this quiz on Functions and Relations. Explore key concepts like domain, range, and the representation of functions using graphical notation and equations. Get ready to reinforce your knowledge and ensure a solid grasp of these foundational math topics.