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# Precalculus: Functions and Graphs, 12th Edition - Earl

Equation of a line: If the slope of a line is given (denoted by ) and if a point on the line is given (coordinate is ), the line equation would be. Reflection in the y-axis: The graph of the function is the graph of reflected in the y-axis. Reflection in the x-axis: The graph of the function is the graph of reflected in the x-axis. Function (from a set X to a set Y A correspondence that associates with each element x (independent variable) of X and a unique element y (dependent variable) of Y. Notation: or.

Composite functions: If is a function from to and is the function from to, then the composite function is the function from to defined by. Inverse functions: Let be a one to one function from to. Domain of a function: The data set of all real numbers for which the correspondence makes sense. One to one functions: is a function from to. Increasing functions: If S is a subset of X and whenever, in S, then is an increasing function in S. Vertical stretching and shrinking: If is a real number, the graph of is the graph of stretched vertically by for or shrunk vertically by for. Horizontal stretching and shrinking: If is a real number, the graph of is the graph of stretched horizontally by for or shrunk horizontally by for. Then, a function from to is called the inverse function of if for all in and for all in.