Functions+&+Graphs

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4-1 Graphing on the Coordinate Plane

**Coordinate plane**- a plane formed by two number lines that intersect at right angles 4-2 Relations and Functions
 * X-axis**- the horizontal axis of the coordinate plane
 * Y-axis**- the vertical axis of the coordinate plane
 * Origin**- the point at which the axes of the coordinate plane intersect
 * Quadrants**- the four parts into which the coordinate plane is divided by its axes
 * Ordered pair**- two numbers that identify the location of a point
 * Coordinates**- the numbers that make an ordered pair and identify the location of a point
 * x-coordinate**- the location of the x-axis of a point in the coordinate plane
 * y-coordinate**- the location of the y-axis of a point in the coordinate plane

**Relation**- any set of ordered pairs (Example: {(5,2); (3,8); (9,6)} This would be a relation) **Function**- a relation that assigns exactly one value in the range to each value of the domain (Example: The above relation is a function. The relation {(2,4); (2, 7); (5,3)} would not be a function because the domain value 2 shows up twice) **Vertical-line Test**- a method used to determine if a relation is a function or not. If a vertical line passes through a graph more than once, the graph is not the graph of a functionThis graph would not be a function because there are multiple points in a straight vertical line
 * Domain**- the domain of a relation is the set of all inputs, or x-coordinates, of the ordered pairs (Example: The domain in the above relation would be 5, 3, 9)
 * Range**- the range of a relation is the set of all outputs or y-coordinates of the ordered pairs (Example: The range in the abov relation would be 2, 8, 6)

4-3 Function Rules, Tables, and Graphs
 * Function rule**- an equation that describes a function (Example: y=4x+2)
 * Function Notation**- to write a rule in function notation, you use the symbol f(x) in place of y (Example: f(x)=4x+2)
 * Independent variable**- a variable that provides the input values of a function (Example: The x-coordinate)
 * Dependent variable**- a variable that provides the output values of a function (Example: The y-coordinate)

4-5 Direct Variation **Direct variation**- a linear function that can be express in the form y=kx, where k≠0  **Constant of Variation for direct variation**- the nonzero constant k in the function y=k x

4-6 Inverse Variation  **Inverse variation**- a function that can be written in the form xy= k or y=k/x. The product of the quantities remains constant, so as one quantity increases, the other decreases.  4-7 Inductive and Deductive Reasoning **Inductive reasoning**- making conclusions based on observed patterns
 * Constant of variation for inverse variation**- the nonzero constant k in the function y= k/ x
 * Conjecture**- conclusion reached by inductive reasoning