chpt 1 Flashcards
define function and give an example
an assignment between 2 separate sets of numbers, such as y=x
define notations and give an example
using a letter as a label for a function, such as y=x+5
what are the types of intervals? briefly describe them
closed, endpoints are included
open, end points are not included
finite, there is a stopping point
infinite, it goes on for infinity
define domain
a collection of allowable inputs for a function
define range
a collection of reachable outputs of a function
what does U represent in (x,y) U (x,a)
union, meaning there is a breaking point for one reason or another in the graph
describe the 3 symmetrical functions briefly
symmetrical wrt y axis, side by side mirror imaging
symmetrical wrt x axis, mirroring above and below
symmetrical wrt origin, 180° rotation around the origin; if point (x,y) exists, then so does (-x,-y)
describe a piecewise function
uses absolute value; has 2 or more formulas, and is V-shaped
what is slope
the change in y over the change in x
what is the point slope equation
y-y1=m(x-x1)
what is the standard form
Ax+By=C
what does Δf represent
shows how much the y-values change
define average rate of change
the fraction of how much f changes over how much x changes
what is the equation for average rate of change
Δf/Δx= f(b)-f(a)/b-a
describe a horizontal shift
if a>0, then the graph of y=f(x-a) is the same as y=f(x) shifted to the right by a.
