General Mathematics Functions Quiz

Study Notes

Functions are utilized to model and represent various real-life scenarios.
Piece-wise functions allow for the description of situations where different conditions apply.

Evaluating functions involves substituting specific values into the function to obtain the output.

Functions can be applied to solve practical problems, using their properties and operations to find solutions.

Rational functions involve the ratio of two polynomials and can model complex scenarios in economics, physics, and other fields.

Distinction between:
- Rational Function: A function expressed as the ratio of two polynomials.
- Rational Equation: An equation involving one or more rational functions.
- Rational Inequality: An inequality that includes rational expressions.

Techniques for solving rational equations often include finding a common denominator, clearing fractions, and applying algebraic manipulation to isolate variables.

Focuses on fundamental concepts in mathematics, including operations, relations, and number systems.
Includes learning competencies such as solving integer operations, identifying functions, and expressing different relations.

Real Numbers: Comprised of rational numbers (e.g., -3, 4/5) and irrational numbers.
Complex Numbers: Combinations of real and imaginary numbers, e.g., (i).
Rational Numbers: Can be expressed as a ratio (quotient), includes integers and fractions.
Integers: Whole numbers including negative, zero, and positive values, e.g., (-5, 0, 7).
Whole Numbers: Natural numbers plus zero, e.g., (0, 1, 2, 3).
Counting Numbers: Natural numbers excluding zero, e.g., (1, 2, 3).
Negative Numbers: Defined as integers less than zero, e.g., (-1, -2).
Operations on Integers: Addition involves keeping the sign for same signs; subtraction involves subtracting magnitudes and adopting the larger sign.
Multiplication and Division Rules: Same signs yield positive results, differing signs yield negative results.

A relation consists of a set of ordered pairs defined by a domain and a range.
Domain: The set of all possible input values, e.g., {1, 2, 3, 4, 5}.
Range: The set of all possible output values, e.g., {1, 3, 5, 7, 9}.
Types of Relations:
- One-to-One: Each element in the domain pairs with one unique element in the range.
- One-to-Many: One element in the domain pairs with multiple elements in the range.
- Many-to-One: Multiple domain elements pair with the same range element.

A function is a specific type of relation where each input from the domain is paired with exactly one output in the range.
Non-functions have at least one input that maps to multiple outputs.