Table of Contents
An Introduction to Relation and Function
A relation is a set of ordered pairs, while a function is a set of ordered pairs where each element in the set corresponds to a unique output. In other words, a function assigns a unique output to every input, while a relation can have repeated outputs for a given input.
What is a Relation?
A relation is a mathematical statement that associates two sets, usually denoted by A and B, with a subset of the Cartesian product A × B. The relation is usually represented by an arrow diagram, with the arrow pointing from A to B. The subset of A × B is typically called the domain of the relation, and the subset of B × A is typically called the range of the relation.
Different Types of Relations in Mathematics
A relation in mathematics is a set of ordered pairs (x, y). The x coordinate is always listed first, followed by the y coordinate. There are many different types of relations that can be studied in mathematics.
One of the most basic types of relations is a linear relation. A linear relation is a relation in which the y coordinate always increases or decreases by the same amount as the x coordinate. For example, the relation y = 2x is a linear relation, because the y coordinate always increases by 2 as the x coordinate increases.
Another basic type of relation is a proportional relation. A proportional relation is a relation in which the y coordinate always increases or decreases by the same percentage as the x coordinate. For example, the relation y = 3x is a proportional relation, because the y coordinate always increases by 3 as the x coordinate increases.
A nonlinear relation is a relation in which the y coordinate does not always increase or decrease by the same amount as the x coordinate. For example, the relation y = x^2 is a nonlinear relation, because the y coordinate increases by the square of the x coordinate.
There are also many different types of special relations that can be studied in mathematics. Some of these relations include:
-Parallel lines: A relation in which the y coordinate of each point is always the same as the y coordinate of the next point.
-Perpendicular lines: A relation in which
What is a Function?
A Function is a set of instructions that tells a computer what to do. Functions can be written in many different programming languages.
Types of Functions-
There are three types of functions-
1. Linear Functions-
A linear function is a function that can be represented by a straight line on a graph. The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
2. Quadratic Functions-
A quadratic function is a function that can be represented by a curved line on a graph. The equation of a quadratic function is y = ax2 + bx + c, where a, b, and c are the coefficients of the function.
3. Exponential Functions-
An exponential function is a function that can be represented by a curved line on a graph. The equation of an exponential function is y = ax, where a is the coefficient of the function.
Some Special Functions in Algebra-
There are a number of special functions in algebra that are used to solve certain types of problems. Some of these functions include the square root function, the cube root function, the absolute value function, and the square function.
Difference between Relations and Functions
Relations can be represented using graphs, while functions cannot. In a relation, each point in the graph corresponds to a unique input and output value. In a function, each point in the graph corresponds to a single input value.
Relations and Functions Notes:
1. A and B are not related
2. A and B are related
3. A is the function of B
4. B is the function of A
Questions to be solved:
1) What is the value of x?
2) What is the value of y?
3) What is the value of z?
1) The value of x is 2.
2) The value of y is 1.
3) The value of z is 3.
