Transformations 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, and how these affect the graph. It also discusses translations of the cube root function in different directions. 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) = 3√x

• f(x) = √x

• f(x) = x^2

• f(x) = x^3

What is the domain of the cube root function?

• x ≠ 0

• x ≥ 0

• x ≤ 0

• All real numbers

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

• It is a translation up 4 units

• It is a reflection over the y-axis

• It is a vertical compression by a factor of 4

• It is a vertical stretch by a factor of 4

How does the graph of f(x) = -3√x differ from the parent function?

• It is a vertical stretch

• It is a vertical compression

• It is a translation down

• It is a reflection over the x-axis

What is the effect of adding 3 to the cube root function?

• Translation down 3 units

• Translation right 3 units

• Translation up 3 units

• Translation left 3 units

What transformation occurs with f(x) = 3√(x - 2)?

• Translation down 2 units

• Translation right 2 units

• Translation up 2 units

• Translation left 2 units

What is the range of all transformed cube root functions?

• y ≥ 0

• All real numbers

• y ≤ 0

• y ≠ 0

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

• None

• One

• Two

• Infinite

What type of symmetry do cube root function graphs exhibit?

• Rotational symmetry

• Reflective symmetry

• No symmetry

• Translational symmetry

If a transformation is of the form y = f(x) - h, what does a negative h indicate?

• Translation down

• Translation left

• Translation up

• Translation right