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makvit [3.9K]
3 years ago
5

A function LaTeX: f\left(x\right)=\sqrt[3]{x}f ( x ) = x 3 is transformed into the function LaTeX: g\left(x\right)=-\sqrt[3]{x}-

8g ( x ) = − x 3 − 8. Name the 2 transformations that occurred and describe the general shape of g(x).
Mathematics
1 answer:
shtirl [24]3 years ago
7 0

Answer:

A reflection in the x-axis, and a vertical translation of 8 units down

Step-by-step explanation:

The given function is

f(x) =  \sqrt[3]{x}

The transformed function is

g(x) =  -  \sqrt[3]{x}  - 8

To see the transformation that occurred, we can rewrite g(x) in terms of f(x).

That is:

g(x) =  - f(x) - 8

Therefore f(x) is reflected in the x-axis and translated 8 units down.

The resulting graph decreases from left to right over its entire domain.

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