Transformations of the Cube Root Function

The video tutorial explains transformations of the cube root function, including vertical and horizontal shifts, vertical stretches, and reflections. It provides examples of each transformation, demonstrating how to graph the transformed functions using key points. The tutorial concludes with a summary of the basic transformations, including reflections, vertical and horizontal shifts, and stretches or compressions.

What is the basic shape of the cube root function graph?

• A circle

• A parabola

• A straight line

• A curve with an S-shape

What effect does adding 2 to the cube root function have on its graph?

• Shifts it down by 2 units

• Shifts it up by 2 units

• Shifts it left by 2 units

• Shifts it right by 2 units

What is the effect of subtracting a constant from the cube root function?

• Shifts the graph left

• Shifts the graph down

• Shifts the graph right

• Shifts the graph up

How does subtracting 2 from the input of the cube root function affect its graph?

• Shifts it right by 2 units

• Shifts it left by 2 units

• Shifts it down by 2 units

• Shifts it up by 2 units

What happens to the cube root function graph when you multiply it by 2?

• It becomes wider

• It becomes narrower

• It shifts down by 2 units

• It shifts up by 2 units

What is the effect of a vertical stretch on the cube root function graph?

• The graph shifts up

• The graph becomes narrower

• The graph shifts down

• The graph becomes wider

What is the result of reflecting the cube root function across the x-axis?

• The graph is shifted down

• The graph is flipped sideways

• The graph is shifted up

• The graph is flipped upside down

How does adding 1 to the input and subtracting 3 from the output of the cube root function affect its graph?

• Shifts it right by 1 unit and up by 3 units

• Shifts it left by 1 unit and up by 3 units

• Shifts it left by 1 unit and down by 3 units

• Shifts it right by 1 unit and down by 3 units

If the cube root function is multiplied by a negative number, what transformation occurs?

• The graph is shifted down

• The graph is reflected across the x-axis

• The graph is reflected across the y-axis

• The graph is shifted up

What happens to the graph of the cube root function when you add a constant to the input?

• It shifts right

• It shifts left

• It shifts down

• It shifts up