Domain and range of composite functions

Lesson 2.1: Domains, Ranges, and Compositions of FunctionsA relation is a relationship between two variables that results in a set of ordered pairs. A is a special kind of relation: it is a relationship between two variables such that each value of the first variable is paired with value of the second variable.The of a function is the set of all possible values of the first variable. The of a function is the set of all possible values of the second variable.You can also use the to determine if a graph represents a function: if every vertical line intersects a given graph at no more than one point, then the graph represents a function.e.g. Which of the following relations are functions? Explain.a) 2,3 , 4,1 , 0,1 , 1,2b) 5, 2 , 1,3 , 0, 4 , 5,1c)d) Relations and functions can also be described using mapping diagramsthat illustrate the pairing between each domain element and its corresponding range element(s).For example, the relation 5, 2 , 1,3 , 0, 4 , 5,1could be described as:510-23-41
If there is a correspondence betweenvalues of the domain, x, and values of the range, y, that is a function, then yfx, and ,xycan be written as ,xfx. The notationsfxand :fxare read as ““. The number represented by fxis the value of the function fat x. For example, afunction fthatis mapping any domain element xto a range element that isequal to21xcan be notated as either 21fxxor :2 1fxx.The variable xis known as the variable, while the variable y, or fx, is known as the variable.e.g. Given the function 2:3gxxx, evaluate:a) 1gb) :2gc) 21gae.g. Given the function 14hxx, find xwhen:a) :9hxb) 37hxae.g.Which of the following relations are functions? Explain.a) b) c) 2yx  d) 31232yxx  510-23-41510-23