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grandymaker [24]
3 years ago
10

Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretch

ing, and/or reflecting. Find the domain and range of the function. f(x) = -(x + 1)3-1

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
8 0

Answer:

Domain and range of the function is all real number.

Step-by-step 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.

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