Cube Root Functions and Their Properties

The video tutorial covers the cube root function, explaining its definition, properties, and how to calculate it. It includes examples of cube and fourth roots, handling negative numbers, and graphing cube root functions. The tutorial also discusses shifting and transformations of graphs, modeling problems using cube root functions, and calculating the average rate of change. Finally, it compares rates of change between different functions.

What is the primary difference between a cube root and a square root?

• Cube root and square root both require three identical numbers.

• Cube root requires two identical numbers, square root requires three.

• Cube root and square root both require two identical numbers.

• Cube root requires three identical numbers, square root requires two.

What is the cube root of 27?

• 5

• 4

• 3

• 2

How does the cube root function graph differ from the square root function graph?

• Cube root graph is a straight line.

• Cube root graph extends only upward.

• Cube root graph is a circle.

• Cube root graph extends both upward and downward.

What is the domain and range of the cube root function?

• Domain: positive numbers only, Range: positive numbers only

• Domain: all real numbers, Range: all real numbers

• Domain: positive numbers only, Range: all real numbers

• Domain: all real numbers, Range: positive numbers only

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

• It moves to the left.

• It moves to the right.

• It moves down.

• It moves up.

If a cube root function is shifted down by 2 units, what is the new important point?

• (0, 2)

• (0, -2)

• (-2, 0)

• (2, 0)

How do you determine the average rate of change for a cube root function?

• By finding the sum of y-values over the sum of x-values.

• By dividing the y-values by the x-values.

• By multiplying the y-values by the x-values.

• By finding the difference in y-values over the difference in x-values.

What is the average rate of change between x = -12 and x = -8 for the function 2(x-3)^(1/3)?

• 0.5

• -1.0

• -0.5

• 1.0

Which function has a greater rate of change between x = -5 and x = 0?

• X^(1/3) - 1

• X - 1^(1/3) + 2

• X + 1^(1/3) - 2

• X^(1/3) + 3

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

• It reflects the graph over the y-axis.

• It shifts the graph to the left.

• It shifts the graph to the right.

• It reflects the graph over the x-axis.