Algebra 2 1.1-1.4

range

The possible values of the output, or dependent variable, of a relation or function.

Function

1. A relationship from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. 2. The action or actions that an item is designed to perform. MEANS Y=

Sequence

A function whose domain is the natural numbers. Eg 3,5,7,9,11

Step graph

A graph that looks like steps. The values are the same for an interval and then "step" to the next interval.

arithmetic sequence

A sequence in which the difference between any two consecutive terms is the same.

explicit definition

Allows you to find any term in the sequence without knowing the previous term. An = a1 + d(n-1)

Transformation of a function

An alteration of a relation (either reflect across axis, stretch/compress, move vertical or horizontal')

Translation

a transformation that shifts or slides every point of a figure or graph the same distance in the same direction without changing the size, shape or rotation

Horizontal compression and stretch

G(x) = f(ax) (graph move closer (stretch) or father away (compression) from y-axis "a" units). Eg. F(1/2x) = 2/1 • x = y

common difference

In an arithmetic sequence, the nonzero constant difference of any term and the previous term. D = 2

{x| x is a real number }

Indicate set {}, x is variable, | means such that

Horizontal translation

Left: g(x) = f(x+h) (subtract h units to x value). Right: g(x) = f(x-h) (add h units to x value) ANY MANIPULATION TO X WILL BE INVERSE OF ORIGINAL SIGH

interval notation

Represent a set of real numbers by the pair of values where the left is the minimum and right is the maximum.

Finite Arithmetic Series

Sn=n/2(a1+an). The Sum of n terms with first term A1 and last term An. the sum of terms in an arithmetic sequence. FOR SUM OF n NUMBERS IN A SEQUENCE, use RECURSIVE FORMULA or add terms

sigma notation

Sum of n terms of a sequence written using... Index i counts through the terms in partial series. Values from 1 up to n, last term in partial series. The value of the ith term is ai. Use explicit formula for the sequence in place of ai

Finite Series

Sum of the terms in a finite sequence. a series with a finite number of terms.

Domain

The possible values for the input of a relation or function

Maximum of a function

The y-value of the highest point on the graph of a function. Point where function change from increasing to decreasing

Minimum of a function

The y-value of the lowest point on the graph of a function. Increasing to decreasing

recursive definition

a sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms. F(n) = f(1), n= 1 and f(n-1) + d, n>1

Vertical translation

Up: g(x) = f(x) + k. Down g(x) = f(x) - k. Move the y value k units

set-builder notation

Verbal description or inequality to describe the numbers of a function's domain or range

Write rule for an absolute value function (1.3)

Write function in form of f(x) = a|x-h| + k to find vertex of function. Then determine slope and equation of each piece on opposite sides of x value. Then write piecewise defined function

X and y intercept

X intercept- line crosses x axis and so y value =0. Y intercept- line cross y axis and x =0

Reflection over axis

Y axis: g(x) = f(-x) (reverse x coordinate and keep y). X axis: g(x) = -f(x) (reverse y coordinate, keep x the same)

What do [] and () mean

[] include the x value when graphing or value and (greater/ less than or equal too) closed. () not include the value when graphing or value. <> closed

piecewise-defined function

a function that has different rules for different parts of its domain. A function that is defined using two or more expressions for different intervals of the domain.

Average rate of change

f(b)-f(a)/b-a. Slope of secant line between two points, use to estimate instantanous rate of change at a point. Slope of a line; y2-y1/x2-x1

vertical stretch/compression

g(x)=af(x). (Graph move closer (compression ) or farther away (stretch) from the x axis)