GEN MATH

• A function is a special kind of relation in which no two distinct ordered pairs have the same first element.
• In an equation in two variables x and y, the variable y may be expressed as f of x if every value of x corresponds to a single value of y.
• The value that a function takes in is called the input or the independent variable.
• The output or the dependent variable is the corresponding value that a function produces.
• There are six kinds of functions: linear, quadratic, constant, identity, absolute, and piecewise.
• A function f is a linear function if f of x is equal to mx plus b where m and b are real numbers.
• The degree or the highest exponent of the variable x is always equal to 1 for a linear function.
• A quadratic function is any equation of the form f of x equals ax squared plus b x plus c where a b and c are real numbers and a is not equal to zero.
• The degree or the highest exponent of the variable x is equal to 2 for a quadratic function.
• A constant function is a function where the variable is removed from the function, leaving only a constant.
• An example of an identity function is f of x equals absolute value of 2x squared.
• An example of an identity function is f of z equals z.
• If a vertical line intersects a given graph at more than one point, then the graph represents a relation that is not a function.
• A constant function has no variable or it's a single number only or a fraction.
• Many to one correspondence is a special case of function where many values of x correspond to one value of y.
• A relation is a set of objects such as numbers grouped with one another which may or may not represent a pattern, simply a set of ordered pairs that are arranged in an orderly manner.
• An identity function is a linear function where m is equal to 1 and b is 0.
• A function is a relation where the value of x is unique for each value of y.
• An example of an identity function is g of h equals h.
• If x is 2, then y is equal to 6.
• In a relation, each value of the independent variable x is unique and is associated with a unique value of the dependent variable, which is represented as y.
• Many to many correspondence is a special case of function where many values of x and y are associated with more than one value of their counterpart.
• A piecewise function or a compound function is a function defined by multiple sub functions where each sub function applies to a certain interval of the main function's domain.
• Vertical line tests can be used to determine if a given graph represents a function or not.
• An example of an identity function is f of x equals absolute value of x plus one.
• An example of an identity function is f of x equals x.
• All functions are relations but not all relations are functions.
• One-to-one correspondence in a relation means that there's one value of x for every value of y, meaning one value of x corresponds to one value of y, making the pairing unique.
• In one to many correspondence, some values of x are associated with more than one value of y.
• One to one correspondence is a special case of function where there is one value of x for each value of y.
• One too many correspondence is a special case of function where one value of x gives many values of y.
• In many to one correspondence, two or more values of x are associated with the same value of y.
• In many to many correspondence, some values of x and y are associated with more than one value of their counterpart.