Algebra2Definitions2.1-2.4

function

a relation in which each element of the domain is paired with exactly one element in the range

one to one function

each element of the domain pairs to exactly one unique element of the range

onto function

each element of the range corresponds to an element of the domain

domain

x values

range

y values

discrete relation

• a relation in which the domain consists of a set of individual elements

• the graph is a set of unconnected points

continuous relation

• a relation when the domain has an infinite # of elements

• the relation can be graphed with a line or smooth curve

vertical line test

• if the vertical line intersects a graph in no more than one point, it’s a function

• if a vertical line intersects a graph in 2 or more points, it is not a function

independent variable

represented by x which is the domain

(usually time)

dependent variable

represented by y, which is the range

function notation

• f(x)

• it replaces y: it’s a more formal way to write an equation

• g(x): same thing

linear function

an equation where:

• no variable is raised to a power other than one

• the graph is a straight line

• the equation can be written in slope-intercept form

nonlinear function

the function includes a set of points that cannot lie on the same line

line symmetry

is present if each half of the graph maps exactly to the other half

line of symmetry

the line dividing the graph into matching halves

point symmetry

is present if the graph of the function can be rotated 180 degrees about a point so that its rotation maps exactly onto itself

point of symmetry

the point which acts as the center of rotation

end behavior

the behavior of a graph as x approaches positive and negative infinity

relative maximum

a point on the graph of a function where no other nearby points have a greater y coordinate

relative minimum

a point on the graph of a function where no other nearby points have a lesser y coordinate

extrema

• “the umbrella”

• turning point

• minima

• maxima

• end behavior