Transformations of the Cube Root Function

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 vertical and horizontal translations, providing examples of how these transformations affect the graph of the cube root function. Finally, the video highlights the attributes of transformed cube root functions, emphasizing their domain, range, and symmetry.

What is the cube root of 8?

• 2

• 4

• 1

• 3

What is the domain of the cube root function?

• All positive numbers

• All negative numbers

• All real numbers

• Only integers

What happens to the graph of the cube root function when it is multiplied by a number greater than 1?

• It stretches vertically

• It shifts right

• It shifts left

• It compresses vertically

How does the graph of the cube root function change when it is multiplied by a negative number?

• It shifts down

• It shifts up

• It reflects over the x-axis

• It reflects over the y-axis

What is the effect of adding a positive constant to the cube root function?

• The graph shifts right

• The graph shifts up

• The graph shifts down

• The graph shifts left

If the cube root function is subtracted by a positive constant, what happens to the graph?

• It shifts up

• It shifts down

• It shifts left

• It shifts right

What is the result of subtracting a positive constant from the input of the cube root function?

• The graph shifts left

• The graph shifts up

• The graph shifts right

• The graph shifts down

What happens to the graph of the cube root function when a positive constant is added to the input?

• It shifts right

• It shifts left

• It shifts up

• It shifts down

What is a common attribute of all transformed cube root functions?

• They have no intercepts

• They have rotational symmetry

• They have no symmetry

• They are only defined for positive x

How many x-intercepts does a transformed cube root function have?

• Infinite

• One

• Two

• None