# Foundations For Functions

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Last updated 5 years ago

Discipline:
Math
Subject:
Algebra I
11   Regression is the study of the relationship beween variables. Correlation is the strength and direction of the linear relationship between two variables. Line of best fit, or line that best fits the data, can be used to make predictions.Correlation coefficient r is a measure of how well the data set is fit by a model.

Foundations for Functions

A transformation is a change in the position, size or shape of a figure. A translation, or slide is a transformation that moves each point in a figure the same distance in the same direction. A reflection is a transformation that flips a figure across a line called the line of reflection. In a horizontal stretch each point is pulled away from the y-axis. The x-coordinate changes. In a horizontal compression each point is pushed toward the y-axis. The x-coordinate changes.In a vertical stretch each point is pulled away from the x-axis. The y-cooridnate changes. In a vertical compression each point is pushed toward the x-axis. The y-coordinate changes.

Chapter 1-1

Chapter 1-2

Chapter 1-3

The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.Constant f(x)=cLinear f(x)=xQuadratic f(x)=x^2Cubic f(x)=x^3Square root f(x)= the square root of x

Horizontal shift f(x)--> f(x-h)Vertical shift (fx)--> f(x) + kReflection across y-axis f(x) --> f(-x) Reflection across x-axis f(x) --> -f(x)Horizonatal sretch/compression by a factor of b. Input value changes. f(x)--> f(1/b x) Vertical stretch/compression by a factor of a. output value changes. f(x) --> a multiplied by f(x)

Chapter 1-4