Transformations and Properties of Cube Root Functions

The video tutorial covers the attributes and transformations of cube root functions. It begins with an introduction to the cube root parent function, explaining its domain, range, and intercepts. The tutorial then explores various transformations, including vertical stretches, compressions, and reflections. It also discusses translations, both vertical and horizontal, and how these affect the graph of the function. Finally, the video highlights the attributes of transformed cube root functions, emphasizing their domain, range, and symmetry.

What is the cube root parent function?

• f(x) = x^3

• f(x) = √x

• f(x) = x^2

• f(x) = 3√x

Which of the following is a perfect cube?

• 9

• 16

• 10

• 27

What is the cube root of -8?

• 2

• 4

• -4

• -2

Where does the cube root function intersect the x-axis?

• (0, 0)

• (1, 0)

• (0, 1)

• (1, 1)

What is the domain of the cube root function?

• All real numbers

• x > 0

• x ≤ 0

• x ≥ 0

What happens to the graph of f(x) = 4 * 3√x?

• It shifts up 4 units

• It stretches vertically by a factor of 4

• It compresses vertically by a factor of 4

• It reflects over the y-axis

What is the effect of multiplying the cube root function by a number less than 1?

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

What transformation occurs with f(x) = -3√x?

• Vertical compression

• Reflection over the y-axis

• Reflection over the x-axis

• Vertical stretch

How does f(x) = 3√x + 3 transform the parent function?

• Shifts left 3 units

• Shifts up 3 units

• Shifts right 3 units

• Shifts down 3 units

What is the transformation for f(x) = 3√x - 2?

• Shift down 2 units

• Shift up 2 units

• Shift right 2 units

• Shift left 2 units