By: IsaBella Combs. Section One: Relation and Functions Domain: a set of all first coordinates. (x-coordinates) Range: a set of all second coordinates.

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Presentation transcript:

By: IsaBella Combs

Section One: Relation and Functions Domain: a set of all first coordinates. (x-coordinates) Range: a set of all second coordinates. (y-coordinates) Relation: set of ordered pairs. Ordered Pair: a pair of coordinates written in (x,y) form Function: a relation in which exactly each element off the domain is paired with exactly one element of the domain. One-To-One: Function: function were each element of the range is paired with exactly one element of the domain. Vocabulary:

Example of ordered pairs: Domain and x-coordinate Range and y-coordinate X Y 2 4

(6,4), (2,-4), (8,1), (0,3) X Y * This is a one-to-one function because all the x elements and the y elements match up!

Linear equations * A linear equation has no operations other than addition, subtraction, and multiplication of a variable by a constant. * A variable cannot be under a radical. The graph of a linear equation is always a line. * A linear equation cannot contain variables with exponents greater than one. * The variables cannot be multiplied together or appear in a denominator.

Linear Equation Example: 4x + 4y = 8 First step is to isolate "x" to one side of the equation by adding 4y to both sides: 4x - 4y + 4y = 8 + 4y 4x = 8 + 4y Second step is to divide both sides by 4: 4x / 4 = (8 + 4y) / 4 x = 2 + y Check your work with the original equation 4 * (2 + y) - 4y = y - 4y = 8 8 = 8

A linear function is a function whose ordered pairs satisfy a linear equation. Linear Functions:

Slope = Rise Run

The slope of a line is the ratio of the change in y-coordinates to the corresponding change in x- coordinates. Rate of change measures how much a quantity changes, on average, relative to the change in another quantity, often time. Slope Examples: