Quiz about Cubic & Cube Root Homework

Question 1

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

Accepted Answer

$$\left(-\infty\ ,\ \infty\right)$$

Answer

$$\left(0\ ,\ \infty\right)$$

Answer

$$\left[0\ ,\ \infty\right)$$

Answer

$$\left[-\infty\ ,\ \infty\right]$$

Question 2

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

Select two correct answers.

Accepted Answer

All Real Numbers

Accepted Answer

$$\left(-\infty\ ,\ \infty\right)$$

Answer

$$y\ \ge\ 0$$

Answer

$$y\ >\ 0$$

Question 3

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.

Accepted Answer

$$g\left(x\right)\ =\ -f\left(x\right)+2$$

Answer

$$g\left(x\right)=f\left(-x+2\right)$$

Answer

$$g\left(x\right)\ =\ f\left(-x\right)+2$$

Answer

$$g\left(x\right)=-f\left(x+2\right)$$

Question 4

Identify the domain of the cube root parent function $$f\left(x\right)\ =\ \sqrt[3]{x}$$ .

Select Two

Accepted Answer

All Real Numbers

Accepted Answer

$$-\infty<x<\infty$$

Answer

$$\left(-10,10\right)$$

Answer

$$-10<x<10$$

Question 5

Identify the range of the cube root parent function $$f\left(x\right)\ =\ \sqrt[3]{x}$$ .

Select Two

Accepted Answer

All Real Numbers

Accepted Answer

$$-\infty<x<\infty$$

Answer

$$\left(-2.154\ ,\ 2.154\right)$$

Answer

$$-2.154<x<2.154$$

Question 6

Identify the function that corresponds with the graph.

Accepted Answer

$$f\left(x\right)\ =\ \sqrt[3]{x+5}+2$$

Answer

$$f\left(x\right)=\sqrt[3]{x+2}-5$$

Answer

$$f\left(x\right)=\sqrt[3]{x-5}+2$$

Question 7

$$f\left(x\right)\ =\ \sqrt[3]{x}$$ has been reflected across the x-axis and shifted down 1 unit to create the graph of g(x).

Accepted Answer

$$g\left(x\right)=-f\left(x\right)-1$$

Answer

$$g\left(x\right)\ =\ -f\left(x\right)+1$$

Answer

$$g\left(x\right)=f\left(x\right)-1$$

Cubic & Cube Root Homework