Algebra 2 Honors Chapter 2 Review

discrete relation

a relation in whicch the domain is a set of individual points
ex. { (1,2),(3,4),(5,6)

continuous relation

a relation that can be graphed with a line or smooth curve
ex. y=2x+3

one to one function

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

how to remember one to one function

“one to one” - unique pairs
(no y values are repeated)

onto functions

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

how to remember onto functons

“onto” - covers all
(every y value is hit)

both onto and one to one functions

each element of the domain is paired to exactly one element of the range, each elemtn of the range corresponds to a unique element of the domain

linear functions

can be written in the form of y=mx+b or f(x) = mx+b
- m and b and real numbers

point of symmetry

a point that you can rotate the graph around and will be symmetric

end behavior

the behavior of a graph as x approaches positive invity or negative infinity

relative maximum

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

relative minimum

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

turning points

the point at which a graph turns; the location of relative maxima or minima, can have multiple

extrema

the maximum or minimum values of a function

positive

a function is positive when above the x-axis

negative

a function is negative when below the x-axis

piecewise-defined function

a function that is written using two or more expressions
ex. f(x) = x+3, if x < 0 ; 2x-7, if x >= 1

step function

a function whose graph is a series of segments

greatest integer function

a step function, where f(x) is the greatest integer less than or equal to x.
(ROUND DOWN)

parent function

the simpliest of a function in a family

vertical translation

f(x)±h

horizonal translation

f(x±h)

f(x) = a ( x - h )² + k

a - reflection across x-axis or dilation
h - horizonal translation
k - vertical translation

vertex

( h , k )

root of the equation

the solution

related function

0 = 2x+3
relation function :
f(x) = 2x+3

related linear function

0 = variable + constant
0 = constant + variable