CHAPTER 4 FUNCTIONS Relation – a set of ordered pairs Domain – The set of all possible input values in a relation or function (the x values of ordered pairs). Range – The set of all possible output values in a relation or function (the y values of ordered pairs).

THINGS TO REMEMBER Remember: x and y are in alphabetical order. Domain and range in alphabetical order. The x values make up the domain, and the y values make up the range. {x|1 < x < 3} is read “all x such that x is greater than or equal to 1 and x is less than or equal to 3.”

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How can I tell if a relation is a function? Vertical Line Test – Graph the function. If you draw a vertical line through any part of the graph it will intersect the graph at no more than one point. Look at the x values – Each value for x (input) can have only one answer for y (output). Map it – You can have no more than one arrow coming out of any input (x value)

Which display is easiest for determining if a relation is a function? Relations can be displayed in four ways: ordered pairs, table, graph, or mapping diagram. The easiest way for me to see if a relation is a function is the vertical line test. What makes the most sense for you? Remember – each x can have only one answer for y.

Vocabulary 4-3 Independent variable – The input of a function. A variable whose value determines the value of the output. Dependent variable – The output of a function. Its value depends on the independent variable. Function rule – an algebraic expression that defines a function.

Function Notation If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function. The dependent variable is a function of the dependent variable. Y is a function of x. Y = f of x.

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Lesson 4-6 Arithmetic Sequences Sequence – a list of numbers that often forms a pattern. Term – Each number in a sequence. Arithmetic Sequence – A sequence whose terms differ by the same nonzero number d. Common Difference – the constant difference of any term and the previous term in an arithmetic sequence.

Finding the nth Term of an Arithmetic Sequence The nth term of an arithmetic sequence with common difference d and first term a 1 is a n = a 1 + (n – 1)d.