Transformations of Cube Root Functions

This video tutorial focuses on graphing cube root functions, starting with the parent function and its properties, such as domain and range. It explains how negative cube root functions reflect over the origin and how transformations like shifts affect the graph. The tutorial also covers correcting the graph direction for negative functions, ensuring an accurate representation.

What is the domain of the parent cube root function?

• All real numbers

• All negative numbers

• All positive numbers

• Only integers

How does the graph of the negative cube root function differ from the parent function?

• It shifts upwards

• It shifts downwards

• It reflects over the origin

• It becomes a straight line

What is the effect of a negative sign inside the cube root function?

• Shifts the graph to the left

• Shifts the graph to the right

• Reflects over the x-axis

• Reflects over the y-axis

What happens to the graph of a cube root function when it is shifted vertically?

• It reflects over the x-axis

• It moves left or right

• It becomes wider

• It moves up or down

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

• Reflection

• Horizontal shift

• No change

• Vertical shift

If a cube root function is shifted one unit to the right, what transformation is applied?

• Vertical shift

• Horizontal shift

• Stretching

• Reflection

What is the new origin of the graph after shifting 2 units left and 3 units up?

• (-2, 3)

• (-3, 2)

• (2, -3)

• (3, -2)

How do you describe the transformation of the function 3 - cube root of (x + 2)?

• Shift 2 units down and 3 units left

• Shift 3 units up and 2 units left

• Shift 2 units up and 3 units right

• Shift 3 units down and 2 units right

How does a negative sign outside the cube root function affect its graph?

• It stretches the graph

• It makes the graph decreasing

• It shifts the graph upwards

• It compresses the graph

Which transformation results in a graph that is a reflection over the x-axis?

• Subtracting a constant outside the function

• Dividing by a constant

• Adding a constant inside the function

• Multiplying by a negative outside the function