Functions PDF

Functions  Function is a relation where each element in the domain is related to only one value in range.  Non-Function is a relation where at least one value in the domain that corresponds to two or more values in the range. One to One One to one function or one to one mapping states that each...

Functions  Function is a relation where each element in the domain is related to only one value in range.  Non-Function is a relation where at least one value in the domain that corresponds to two or more values in the range. One to One One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then f is one to one. One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then f is one to one. One to One Many to One A function is called many-to-one (sometimes written 'many- one') if some function output value corresponds to more than one input value. In symbols, the function f is many-to-one if there are two distinct values a and b in the domain of f such that f(a)=f(b). Many to One NOTE: * One – To – Many is NOT A FUNCTION Types of Function 1. Linear Function Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. mx + b or ax + b Examples: a. f(x) = 7x + 1 b. g(x) = x + 3 2. Quadratic Functions A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. In other words, a quadratic function is a “polynomial function of degree 2.” ax² + bx + c  Examples a. f(x)= x²- 6x+ 5 b. g(x)= 2x²+2x- 3 3. Polynomial Function A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.  Example: a. f(x) = x^4+2x+1 b. g(x) = 3x^3-7  Piecewise Function Defined by multiple sub-functions, and each sub function applying to a certain interval of the main function’s domain, the sub-domain. f (x) = 3x + 5 ; -4 ≤ x ≤ -1 = 2 ; -1 ≤ x < 3 = -x + 2 ; 3 ≤ x ≤ 4 A user is charged P300 monthly for a particular mobile plan, which includes 100 free text messages. Messages in excess of 100 are charged P1 each. Represent the amount a consumer pays each month as a function of the number of messages m sent in a month Solution. Let t(m) represent the amount paid by the consumer each month. It can be expressed in piecewise function:  Evaluating Function Think of the domain as the set of the function’s input values and the range as the set of the function’s output values as shown in the figure below. The input is represented by x and the output by f(x). Example: Evaluate each = f(x) = x + 8 a. f(4) = f(4) = x + 8 = b. f(–2) = f(-2) = x + 8 = c. f(–x) = f(-x) = x + 8 = d. f(x + 3) = f(x + 3) = x + 8 = QUIZ 1: FUNCTION OR NOT FUNCTION