Essential Ideas Lesson 2.1 Functional Notation Functional notation is used to identify functions as f(x), which is read as “f of x”. f(x) is the value.

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Presentation transcript:

Essential Ideas Lesson 2.1 Functional Notation Functional notation is used to identify functions as f(x), which is read as “f of x”. f(x) is the value of the function f at x. The independent variables of a function are the input values are the dependent variables are the output values.

Essential Ideas Lesson 2.2 Introduction to Sequences A mathematical sequence is a function with a domain that is the set of counting numbers Sequences can be defined using words, equations, tables, graphs, diagrams, and figures. The nth The nth term or general term of a numerical sequence can be defined by an explicit formula. A numerical sequence can be defined by a recursive formula.

Essential Ideas Lesson 2.3 Arithmetic and Geometric Sequence An arithmetic sequence is a sequence in which each term is calculated from the previous term by adding a constant. The constant that is added in an arithmetic sequence is the common difference. The explicit formula for an arithmetic sequence is The recursive formula for an arithmetic sequence is A geometric sequence is a sequence in which each term is calculated from the previous term by multiplying by a constant. A geometric sequence is a sequence in which each term is calculated from the previous term by multiplying by a constant.

Lesson 2.3 continued The constant that is multiplied in a geometric sequence the common ratio. The explicit formula for a geometric sequence is The recursive formula for a geometric sequence is The recursive formula for a geometric sequence is

Essential Ideas Lesson 2.4 Domains and Ranges of Algebraic Functions Domains of functions are determined by the values of the independent variable by the define the function. Ranges of functions are determined by the possible values of the dependent variable.

Essential Ideas Lesson 2.5 Extrema and Symmetry The x-intercept(s) is(are) the point(s) where the graph of a relation or function intersects the x-axis and where the value of the dependent variable is 0. The y-intercept(s) is(are) the point(s) where the graph of a relation or function intersects the y-axis and where the value of the independent variable is 0. Extreme points are maximum and minimum values of the relation or function. A line of symmetry divides a relation or function into two mirror image halves.

Essential Ideas Lesson 2.6 Rates of Change of Functions The average rate of change of a function between two points of the function’s graph is the change in the dependent variables divided by the change in the independent variable. The slope of a linear function is the unit rate of change and is constant. For non-linear functions, the unit rate of change is an average rate and is not constant.