#A = "Amplitude"##2pi//B = "Period"##-C//B = "Phase shift"##D = "Vertical shift"#

The maximum domain that a duty is provided by every the values in which it is fine defined:

#"Domain" = x #

Since the sine role is identified everywhere top top the actual numbers, its collection is #RR#.

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As #f# is a routine function, its variety is a bounded interval given by the max and min values of the function. The maximum output of #sinx# is #1#, while its minimum is #-1#.

Hence:

#"Range" = or "Range" = #

The range depends ~ above the authorize of #A#. However, if we enable that

# = #

then the selection is more simply identified as .

As a conclusion,

#f:RR -> #

Sridhar V.
Jul 26, 2018

#" "#Domain:

#color(blue)((-oo

Interval Notation: #color(green)((-oo, oo)#

Range:

#color(blue)((-1

Interval Notation: #color(green)(<-1, 1>#

Explanation:

#" "#Domain and selection of a SIN Graph:

Let us look in ~ the SIN Graph first:

#color(blue)("Domain :"#

The domain of a function is the set of input values because that which the role is real and defined.

#color(blue)((-oo

Domain restriction provided for the SIN Graph to display screen ONE finish cycle.

#color(blue)("Range :"#

The set of output values (of the dependency variable) because that which the role is defined.

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As girlfriend can easily observe, the SIN graph go up till #color(blue)(1# and goes down until #color(blue)(-1#

#color(blue)((-1

Hope this helps.