Question

Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Find the domain and range of the function. f(x) = -(x + 1)3-1

Answer 1

Domain and range of the function is all real number.

Explanation:

The given function is

`f(x)=-(x+1)^3-1` .... (1)

It is a cubic function.

The parent cubic function is

`g(x)=x^3`

The translation is defined as

`h(x)=k(x+a)^3+b` .... (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.