Sets and Numbers Overview

A set of all positive whole numbers, starting at 1 and increasing without limit. These numbers are used for counting and ordering.

A set of all whole numbers, including both positive and negative integers, and zero. They represent both positive and negative quantities.

A set of numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They represent whole numbers and parts of whole numbers.

Numbers that cannot be expressed as a fraction of two integers. They cannot be represented as a terminating or repeating decimal.

The set of all rational and irrational numbers. They represent all possible numbers on a number line.

A set of numbers that includes the imaginary unit 'i', which is the square root of -1. These numbers can be expressed as a sum of a real and an imaginary part.

A collection of elements, where each element is unique and well-defined. Sets are denoted by curly braces.

A relationship between sets, where every element of one set is also an element of the other set. It is denoted by ⊆.

A rule that associates each element in a set called the ‘domain’ with a unique element in another set called the ‘range’.

The set of all possible input values for a function, represented by 'Df' or 'Dom(f).'

The set of all possible output values for a function, represented by 'Rf' or 'Ran(f).'

A function that assigns a constant value to every input. It has a horizontal line as its graph.

A function that involves the square of the input variable. Its graph is a U-shaped curve.

A function that involves the square root of the input variable. Its graph is a curve that starts at the origin and increases slowly.

A function that involves taking the absolute value of the input variable. Its graph is a V-shaped curve.

A function that involves a rational expression, where both numerator and denominator are polynomials. Its graph can have vertical and horizontal asymptotes.

The representation of a function using points plotted on a coordinate system based on ordered pairs (x,f(x)).

The process of finding the domain of a function by identifying when it is defined. It involves considering restrictions on the input values.

The process of finding the range of a function by determining the set of all possible output values. It involves analyzing the function's behavior over its domain.

The process of sketching the graph of a function based on its definition and properties. It involves plotting points and connecting them to form a curve.

The mathematical idea that a function can be represented by a set of ordered pairs (x,y), where x represents the input and y represents the output.

The process of identifying the limitations or restrictions on the input values of a function. It involves considering factors such as square roots, fractions, and logarithms.

The process of determining the behavior of a function as the input values approach infinity or negative infinity. It involves analyzing the function's growth or decay patterns.

The process of identifying any values of x that make the denominator of a rational function equal to zero. These values must be excluded fromthe domain.

The process of simplifying a given function by performing algebraic operations or using trigonometric identities. It involves expressing the function in a more compact or manageable form

The process of examining different aspects of a function, such as its domain, range, intervals of increasing and decreasing behavior, intercepts, and asymptotes. It involves understanding the function's properties and its graphical representation.

The process of applying a function to a specific input value. It involves substituting the input value into the function's formula and evaluating the result.

The process of finding the inverse of a function by swapping the roles of the input and output variables. It involves solving for the input variable in terms of the output variable.