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8. State the order and type of each transformation of the graph of the f(x) = - (x + 1) ^ 3 + 1 as compared to the graph of the base function.

User Erkan BALABAN
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1 Answer

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The base function is: f(x) = x³

f(x + a) translates f(x) a units to the left. Then, f(x + 1) = (x + 1)³ translates f(x) 1 unit to the left.

-f(x) reflects f(x) about the x-axis. Then, -f(x + 1) = -(x + 1)³ reflects f(x) about the x-axis.

f(x) + b translates f(x) up b units. Then: -f(x + 1) + 1 = -(x + 1)³ + 1 translates f(x) up 1 unit.

In conclusion, the order of transformations is:

left 1 unit, reflection about the x-axis, up 1 unit.

User Harry Ninh
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