Foundations For Functions

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Last updated 4 years ago

Algebra I

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Foundations For Functions

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

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Real World Applications:Businesses use regression to predict things such as future sales, stock prices, currency exchange rates, and productivity gains. If you can't decide what phone plan to choose you could graph a linear function of both phone plans to see what plan is cheapest for you. Construction workers use transformations when they have to relocate a building. For example, they may have to rotate a building to face it towards a different direction or they may have to translate a building a couple of blocks away.Civil engineers must learn linear algebra which involves linear transformations and quadratic forms. They use linear correlation and regression analysis to quantify risk and safety in their designs.


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