Answer:
Domain and range of the function is all real number.
Step-by-step explanation:
The given function is
[tex]f(x)=-(x+1)^3-1[/tex] .... (1)
It is a cubic function.
The parent cubic function is
[tex]g(x)=x^3[/tex]
The translation is defined as
[tex]h(x)=k(x+a)^3+b[/tex] .... (2)
where, k is stretch factor, a is horizontal shift and b is vertical shift.
If |k|>1, then the graph of g(x) stretch by factor k and if 0<|k|<1
, then the graph of g(x) compressed by factor k. If k<0, then graph of g(x) reflects across x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2), we get
k=-1<0, so the graph reflects across x-axis.
a=1>0, so the graph of parent function shifts 1 units left.
b=-1<0, so the graph of parent function shifts 1 units down.
Domain and range of cubic polynomial is all real number. Since the given function is a cubic polynomial, therefore domain and range of the function is all real number.
