Terms Notes # Alpha 0
Alpha 1 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:
Excluded values:
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. real numbers when substituted in for “x” will give an imaginary number for “y” or be undefined.
Alpha 2 Composition of Functions:
Iteration:
Given functions f and g, the composite function f ◦ g can be described by the following equation: [f ◦ g](x) = f(g(x))
The composition of a function to itself. Two functions f and g are this iff [f ◦ g](x) = [g ◦ f](x) = x.
Inverse functions:
Property of Inverse Functions:
Suppose f and f-1 are this. Then, f(x) = y iff f-1(y) = x.
Alpha 3 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: X-intercept:
values of x for which f(x) = 0. (These are the x-intercepts.)
The point at which a graph crosses the x-axis. In a linear function, this will have coordinates b ,0 . m
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.
Alpha 4 Pythagorean Theorem:
In a right triangle, the sum of the squares of each leg equals the square of the hypotenuse.
Distance Formula for Two Points:
k units between two points with coordinates (x1, y1) and (x2, y2) is given by the following formula. k ( x2 x1 )2 ( y2 y1 )2 Linear Relationships & Functions Page 1 of 2
Terms Slope:
this is the ratio of the change in the y-values of the coordinates of the points to the corresponding change in x-values.
Midpoint of a Line Segment:
If the coordinates of A and B are (x1, y1) and (x2, y2), respectively, then this of AB has coordinates x1 x2 , y1 y2 2 2
Alpha 5 Slope-Intercept Form: y-intercept:
This form of an equation of a line is y = mx + b. The slope is m and y-intercept is b.
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. y - y1= m(x - x1)
Alpha 6 Parallel Lines:
Two nonvertical lines are this iff their slopes are equal. Any two vertical lines are always this.
Standard Form of a Linear Equation:
Perpendicular Lines:
The standard form of a linear equation is +Ax + By = C, where A, B, and C are integers and A and B are both not zero.
Two nonvertical lines are this iff their slopes are negative reciprocals.
Linear Relationships & Functions Page 2 of 2