Functions and Relations: A Comprehensive Guide for High School Mathematics, Slides of Mathematics

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CHAPTER 1: General Mathematics Course

FUNCTIONS AND

RELATIONS

LESSON OUTLINE

• (^) Definition of a function and relation
• (^) Types of relation
• (^) Piecewise defined function
• (^) Operations in Functions
• (^) Inverse Functions
• (^) Rational Functions

LESSON OUTLINE

• (^) Logarithmic Inequalities
• (^) Graphs of Rational, Exponential, and Logarithmic Functions

DEFINITION OF FUNCTION

• (^) It is a mathematical expression

that has a domain and range and

it complies with the vertical line

test that intersect the points in a

curve at least once.

EXAMPLE OF FUNCTIONS

• (^) Polynomial Functions – this function can be a linear, quadratic, cubic, quartic, quintic, and so on…
• (^) Absolute Function – expression that has a modulus denoting the absolute value.

EXAMPLE OF FUNCTIONS

• (^) Rational Function – it is the ratio of two polynomials given that the polynomial in the denominator cannot be equal to 0.
• (^) Exponential Function – it can be classified in to two different types. It varies in the sign of the exponent of any base.

DEFINITION OF RELATION

• (^) Relation – is a collection of ordered pairs.
• (^) Ordered pairs – it is a pair of the domain and the range usually enclosed by parenthesis, such that (x,y) can be an example. It could be a set of relation (e.g. (2,3),(4,3),(6,2),…).

TYPES OF RELATION

• (^) ONE TO ONE
• (^) ONE TO MANY
• (^) MANY TO ONE
• (^) MANY TO MANY

TYPES OF RELATION

OPERATIONS OF

FUNCTIONS

ADDITION OF FUNCTIONS

• (^) The sum of the functions can be

written f(x) + g(x) or as (f + g)(x).

SUBTRACTION OF FUNCTIONS

• (^) The difference of the functions can be written f(x) – g(x) or as (f – g)(x).

DIVISION OF FUNCTIONS

• (^) The quotient of two functions f(x) and g(x) provided that g(x)≠0. In such reason that the whole function will be undefined. It can be written as f(x)/g(x) or as (f/g)(x).
• (^) (g(x)/f(x)) or (g/f)(x)

COMPOSITION OF FUNCTIONS

• (^) A composition of function is created when one function is substituted with another function.
• (^) Is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function.