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Relation a pairing of elements of one set with elements of a second set. This is usually expressed as a set of ordered pairs.
Domain the set of all abscissas (the first value in the ordered pair) of the ordered pairs.
Range the set of all ordinates (the second value in the ordered pair) of the ordered pairs.
Function this is a relation in which each element of the domain is paired with exactly one element in the range.
Function Notation The symbol f(x) is read “f of x”. f(x) = y, therefore the ordered pairs of a relation are in the form (x, y) or (x, f(x)).
Vertical Line Test If every vertical line drawn on the graph of a relation passes through no more than one point on the graph, then the relation is a function.
Excluded values real numbers when substituted in for “x” will give an imaginary number for “y” or be undefined.
Composition of Functions Given functions f and g, the composite function f ◦ g can be described by the following equation: [f ◦ g](x) = f(g(x))
Iteration The composition of a function to itself.
Inverse functions Two functions f and g are this iff [f ◦ g](x) = [g ◦ f](x) = x.
Property of Inverse Functions Suppose f and f1 are this. Then, f(x) = y iff f-1 (y) = x.
Linear Equation This has the form Ax + By = C, where A and B are both not zero. The graph is always a line.
Solution of a Linear Equation An ordered pair that makes the equation true. Each ordered pair corresponds to a point in the coordinate plane.
Linear Function This is defined by f(x) = mx + b, where m and b are real numbers.
Zeros of the Function f values of x for which f(x) = 0. (These are the x-intercepts.)
X-intercept The point at which a graph crosses the x-axis. In a linear function, this will have coordinates
Constant Function A function f is this if f(x) = b. The graph is a horizontal line. This either has no zeros (b ≠ 0)or every value of x is a zero (b = 0).
Linear Inequality This has the form Ax + By + C < 0, Ax + By > C, Ax + By > C, or Ax + By < C, where A and B are both not zero. The graph consists of a boundary and the shading of a region.
Pythagorean Theorem In a right triangle, the sum of the squares of each leg equals the square of the hypotenuse.
Slope-Intercept Form This form of an equation of a line is y = mx + b. The slope is m and y-intercept is b.
y-intercept The point where the graph crosses the y-axis.
Point-Slope Form If the point with coordinates (x1, y1) lies on a line having slope m, this form of the equation of the line can be written as follows.
Created by: love.ross