Functions Flashcards
transformation of f (x) + a?
translation 0i + aj
transformation f (x+a)?
translation -ai + 0j
transformation k f (x)?
stretch in y direction, SF k
transformation f (k x)?
stretch in x direction SF 1/k
transformation - f (x)?
reflection in x axis
transformation f (-x)
reflection in the y axis
how do you describe a translation (exam)?
word translation followed by a column vector
how do you describe a stretch or squash (exam)?
word stretch, followed by stretch factor: (…) then direction
how do you describe a reflection (exam)?
word reflection followed by eq. of reflection line or axis name
what is a mapping?
any rule which assigns an input to an output
(eg. y = x+3)
what is the domain?
set of possible inputs (x values)
what is the range?
set of all possible outputs (y values)
what is an input/object?
x value put into function
what is an output/image?
y value given from a function
what is a one to one?
one input gives one outrput, one output comes from one input
what is a many to one?
more than one input gives a particular output
what is a one to many?
one input gives many outputs
what is a function?
a mapping that is one-one or many-one. cannot be one-many
what is continuity?
function is continuous if it has no breaks
what is a piecewise?
a single funtion which has different rules for different parts of its domain
what are examples of mapping graphs?
what are end points?
if the domain is restricted, these are the points at the end of an interval
how do you deal with a piecewise function?
“chop it up” and apply the functions to the specified areas of the domain
what is a composite function?
a function of a function (ie. putting the inside function into wherever theres an x in the outside function
