Graphing Transformations of the Cube Root Function

This video tutorial covers transformations of the cube root function, including vertical and horizontal shifts, vertical stretches and compressions, and reflections across axes. It provides examples and explains how to graph these transformations using key points. The tutorial concludes with a summary of the basic transformations.

What is the basic graph discussed in the introduction of the cube root function?

• Sine function

• Cube root function

• Quadratic function

• Linear function

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

• Shifts down

• Shifts up

• Shifts right

• Shifts left

What happens to the graph of the cube root function when you add 2 to each y-coordinate?

• It compresses vertically

• It shifts down

• It shifts up

• It stretches vertically

How does subtracting a constant from the input x in the cube root function affect the graph?

• Shifts up

• Shifts left

• No shift

• Shifts right

If you subtract 2 from each x-coordinate in the cube root function, where does the graph move?

• Down 2 units

• Right 2 units

• Left 2 units

• Up 2 units

What is the result of multiplying the cube root function's output by 2?

• Vertical compression

• Horizontal stretch

• Vertical stretch

• Horizontal compression

What does the transformation y = 2 * cube root of x do to the graph compared to the basic function?

• Stretches it vertically

• Compresses it vertically

• Moves it left

• Moves it right

What transformation occurs when the cube root function is multiplied by -1?

• Vertical shift down

• Reflection across the X-axis

• Vertical shift up

• Reflection across the Y-axis

What is the effect of the transformation y = -cube root of x on the graph?

• Reflects across the X-axis

• Reflects across the Y-axis

• Shifts down

• Shifts up

How does adding 1 to x and subtracting 3 from y in the cube root function affect the graph?

• Shifts right 1 unit, up 3 units

• Shifts left 1 unit, down 3 units

• Shifts left 1 unit, up 3 units

• Shifts right 1 unit, down 3 units