Cubic & Cube Root Homework

Identify the domain of the cubic parent function $$f\left(x\right)\ =\ x^3$$

Identify the range of the cubic parent function $$f\left(x\right)\ =\ x^3$$ .

Select two correct answers.

The domain for the function $$f\left(x\right)\ =\ \frac{1}{3}\left(x-2\right)^3+4$$ is ​ (a)   while the range is $$\left(-\infty,\infty\right)$$ .

The domain for the function $$f\left(x\right)\ =\ \frac{1}{3}\left(x-2\right)^3+4$$ is ​ (a)   while the range is $$\left(-\infty,\infty\right)$$ .

The function $$f\left(x\right)=x^3$$ was ​ (a)   by a factor of 1/3, shifted ​ (b)   2 units, and shifted ​ (c)   4 units to create the function $$g\left(x\right)\ =\ \frac{1}{3}f\left(x-2\right)+4$$ .

Identify the equation of the function $$f\left(x\right)\ =\ x^3$$ that has been reflected across the x-axis, and shifted 2 units up.

$$3^3\ =\$$

$$\left(-1\right)^3$$

$$4^3$$

$$\left(\frac{1}{2}\right)^3=$$