Precalculus Chapter 1 Vocabulary

Relation

A set of ordered pairs, where elements from one set (domain values) are paired with elements from another set (range values)

Domain

The first element of an (x, y) ordered pair; the set of all INPUT values for a given function

Range

The second element of an (x, y) ordered pair; the set of all OUTPUT values for a given function

Function

A relation in which each element in the domain is paired with one, and only one, element in the range; each INPUT has only ONE OUTPUT.

Function Notation

y = 3x + 2 can also be expressed as f(x) = 3x + 2, where f(x) is read "f of x," and x represents the domain (INPUT values)

Vertical Line Test

Applied to the graph of a relation, this is a quick way to determine whether the relation is also a function.

Composition

Means of combining functions by inserting one function as the input for a second function and simplifying. Notation [f o g](x) = f ( g(x) )

Linear Equation

Any equation that can be written in the form Ax + By + C = 0, where the (x, y) solutions to the equation form a straight line when graphed.

X-Intercept

The point where the graph of a linear equation crosses the horizontal axis.

Y-Intercept

The point where the graph of a linear equation crosses the vertical axis.

Slope

The ratio of the vertical change to the horizontal change between two points; "rise over run"; rate of change;

m = (y2 - y1) / (x2 - x1)

Linear Equation in Standard Form

Ax + By = C

Linear Equation in Slope-Intercept Form

y = mx + b

Interpretation of Slope-Intercept Form Equation

m = slope, b = y-intercept, x and y are (x, y) ordered pairs that are solutions to the given equation and show up as points on the graph of the line

Zeros of a Function

The x-value(s) for which the function is equal to zero; on a graph, they appear as the x-intercepts

Linear Equation in Point-Slope Form

y - y1 = m(x - x1)

Interpretation of Point-Slope Form Equation

m = slope, (x1, y1) is a point through which the line passes, and x and y are other (x, y) ordered pairs that are solutions to the given equation

Parallel Lines

Two lines that share the same slope and thus have no points in common

Perpendicular Lines

Two lines which intersect at a 90 degree angle; their slopes are opposite reciprocals of one another

Piecewise Function

Generated by using different equations for different intervals of the domain