4.7 Arithmetic Sequences

Video Notes

Assignment

Vocabulary

sequence - an ordered list of numbers

term in a sequence - a number in a sequence

arithmetic sequence - an ordered list of numbers in which the difference between each pair of consecutive terms is the same

common difference - the difference between each pair of consecutive terms is an arithmetic sequence

Video Notes

Assignment

Vocabulary

sequence - an ordered list of numbers

term in a sequence - a number in a sequence

arithmetic sequence - an ordered list of numbers in which the difference between each pair of consecutive terms is the same

common difference - the difference between each pair of consecutive terms is an arithmetic sequence

3.7 Transformations of Graphs of Linear Functions - Day 1

Video Notes

Assignment

Vocabulary

family of functions - a group of functions with similar characteristics

parent function - the most basic function in a family of functions.

transformation - changes the size, shape, position or orientation of a graph

translation - a transformation that shifts a graph horizontally or vertically, but doesnt change the size, shape or orientation of the graph

reflections - a transformation that flips a graph over a line called the line of reflection

horizontal shrink - a transformation that causes the graph of a function to shrink toward the y-axis when all the x-coordinated are multiplied by a factor a, where a > 1. (steeper line) y = f(ax) (y-intercept stays the same)

horizontal stretch - a transformation that causes the graph of a function to stretch away from the y-axis when all the x-coordinates are multiplied by a factor a, where 0 < a < 1. (flatter line) y = f(ax) (y-intercept stays the same)

vertical stretch - a transformation that causes the graph of a function to stretch away from the x-axis when all the y-coordinates are multiplied by a factor a, where a > 1. (steeper line) y = (a) f(x) (x-intercept stays the same)

vertical shrink - a transformation that causes the graph of a function to shrink toward the x-axis when all the y-coordinates are multiplied by a factor a, where 0 < a < 1 (flatter line) y = (a) f(x) (x-intercept stays the same)

Video Notes

Assignment

Vocabulary

family of functions - a group of functions with similar characteristics

parent function - the most basic function in a family of functions.

__(linear parent function__: y = x)transformation - changes the size, shape, position or orientation of a graph

translation - a transformation that shifts a graph horizontally or vertically, but doesnt change the size, shape or orientation of the graph

__horizontal translation__: y = f(x - h)__vertical translation:__y = f(x) + kreflections - a transformation that flips a graph over a line called the line of reflection

__reflections in x-axis__: y = -f(x)__reflections in y-axis__: y = f(-x)horizontal shrink - a transformation that causes the graph of a function to shrink toward the y-axis when all the x-coordinated are multiplied by a factor a, where a > 1. (steeper line) y = f(ax) (y-intercept stays the same)

horizontal stretch - a transformation that causes the graph of a function to stretch away from the y-axis when all the x-coordinates are multiplied by a factor a, where 0 < a < 1. (flatter line) y = f(ax) (y-intercept stays the same)

vertical stretch - a transformation that causes the graph of a function to stretch away from the x-axis when all the y-coordinates are multiplied by a factor a, where a > 1. (steeper line) y = (a) f(x) (x-intercept stays the same)

vertical shrink - a transformation that causes the graph of a function to shrink toward the x-axis when all the y-coordinates are multiplied by a factor a, where 0 < a < 1 (flatter line) y = (a) f(x) (x-intercept stays the same)

6.3 Exponential Functions
Video Notes Assignment Vocabulary exponential function - a nonlinear function of the form y = ab^x where a≠0, b ≠1 and b >0 asymptote - a line that a graph approaches but never intersects |

6.4 Exponential Growth and Decay
Video Notes Assignment Vocabulary exponential growth - occurs when a quantity increases by the same factor over equal intervals of time exponential growth function - a function of the form y=a(1 +r)t, where a > 0 and r > 0 exponential decay - exponential decay - occurs when a quantity decreases by the same factor over equal intervals of time. exponential decay function - a function of the form y=a(1 −r)t, where a > 0 and 0 < r < 1 compound interest - the interest earned on the principal and on previously earned interest. |

6.5 Geometric Sequences
Video Notes Assignment Vocabulary geometric sequence - an ordered list of numbers in which the ratio between each pair of consecutive terms is the same common ratio - the ratio between each pair of consecutive terms in a geometric sequence |

6.6 Recursively Defines Sequences
Video Notes Assignment Vocabulary explicit rule - a rule to define arithmetic and geometric sequences that gives a∨n as a function of the term's position number n in the sequence recursive rule - a rule to define arithmetic and geometric sequences that gives the beginning term(s) of a sequence and a recursive equation that tells how a∨n is related to one or more preceding terms |

(7.1) & 7.2 Multiplying Polynomials
Video Notes Assignment Vocabulary monomial - a number, a variable, or the product of a number and one or more variables with whole number exponents degree of a monomial - the sum of the exponents of the variables in the monomial The degree of a nonzero constant term is 0. The constant 0 does not have a degree. polynomial - a monomial or a sum of monomials. (each monomial is called a term) binomial - a polynomial with two terms trinomial - a polynomial with three terms degree of a polynomial - the greatest degree of its terms standard form of a polynomial - a polynomial of one variable written with the exponents of the terms decreasing from left to right. leading coefficient - the coefficient of the first term closed - when an operation performed on any two numbers in the set results in a number that is also in the set FOIL method - a shortcut for multiplying two binomials by finding the sum of the products of the first terms, outer terms, inner terms, and last terms. (also called double distributive or box method) |

7.4 Dividing Polynomials
Video Notes Assignment Vocabulary polynomial long division - a method to divide a polynomial f(x) by a nonzero divisor d(x) to yield quotient polynomial q(x) and a remainder r(x). synthetic division - a shortcut method to divide a polynomial by a binomial of the form x - k |

7.5 Solving Polynomial Equations in Factored Form
Video Notes Assignment Vocabulary factored form - a polynomial that is written in a product of factors zero-product property - if the product of two real numbers is 0, then at east one of the numbers is 0 roots - solutions of a polynomial equation repeated roots - two or more roots of an equation that are the same number |

7.8 Factoring Special Products
7.9 Factoring Polynomials Video Notes Assignment Vocabulary factoring by grouping - to use the distributive property to factor a polynomial with four terms factored completely - a polynomial that is written as a product of unfactorable polynomials with integer coefficients |