Cube Root Functions and Transformations

The video tutorial covers the cube root parent function, its inverse relationship with the cubic function, and how to graph it. It explains the domain and range, which are all real numbers, and discusses the function's symmetry. The video also explores transformations of the cube root function, providing examples with different transformations, such as negative 2 cube root x plus 4 and cube root x minus two plus one. These examples illustrate how transformations affect the graph's appearance and intercepts.

What is the inverse of the cubic function y = x^3?

• y = x^2

• y = cube root of x

• y = 1/x

• y = x^3

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

• A circle

• A sideways S

• A parabola

• A straight line

What type of symmetry does the cube root function exhibit?

• Symmetry about the y-axis

• No symmetry

• Rotational symmetry

• Reflective symmetry

What is the domain of the cube root function?

• All real numbers

• x ≤ 0

• x ≥ 0

• x ≠ 0

What is the range of the cube root function?

• y ≥ 0

• y ≤ 0

• All real numbers

• y ≠ 0

What does a negative sign outside the cube root function indicate?

• A reflection over the y-axis

• A reflection over the x-axis

• A horizontal stretch

• A vertical compression

What does a vertical stretch by a factor greater than 1 do to the graph?

• Makes it wider

• Reflects it over the x-axis

• Makes it narrower

• Reflects it over the y-axis

In the function y = cube root(x - 2) + 1, what does the '-2' inside the cube root indicate?

• A shift left by 2 units

• A shift right by 2 units

• A shift up by 2 units

• A shift down by 2 units

In the function y = cube root(x - 2) + 1, what does the '+1' outside the cube root indicate?

• A shift right by 1 unit

• A shift up by 1 unit

• A shift down by 1 unit

• A shift left by 1 unit

What is the new y-intercept of the function y = -2 * cube root(x + 4)?

• (0, 0)

• (0, -3)

• (0, 3)

• (0, -2)