Question 1181062

{{{f(x)=Asin(Bx+C)+D}}}

Where
{{{A}}}=Amplitude
{{{2pi/B}}}=Period
{{{C/B}}}=Phase shift
{{{D}}}=Vertical shift

Range=[{{{D-A}}},{{{A+D}}}]
or
Range=[{{{A+D}}},{{{D-A}}}]

{y|y ∈ R,-6 ≤ y ≤ 0}

{{{D-A=-6}}}
{{{D=A-6}}}............eq.1

{{{A+D=0}}}
{{{A=-D}}} ....eq.2

=>{{{D=A-6}}}=>{{{D=-D-6}}}=>{{{2D=-6}}}=>{{{D=-3}}}
=>{{{A=-(-3)=3}}}
Period of sine function is {{{2pi}}}

{{{2pi/B=2pi}}}=>{{{B=1}}}

Phase shift
{{{C/B=0/1}}}=>{{{C=0}}}

{{{f(x)=3sin(x)-3}}}

the equation of the central axis: {{{y=-3}}}