Cube Root Functions and Graphing

This video tutorial explains how to graph cube root functions over a restricted domain. It begins with an introduction to cube root functions and the concept of a restricted domain. The tutorial then provides a detailed example of graphing the function y = ∛(x-2) for the domain from -6 to 10. It covers creating a table of values, plotting integer points, and constructing the graph with a curved line. The video also highlights common mistakes, such as connecting points with straight lines, and emphasizes the importance of not including arrows on the endpoints due to the restricted domain.

What is a restricted domain in the context of graphing functions?

• A domain that includes all real numbers

• A domain that excludes zero

• A domain that is limited to a specific range of x-values

• A domain that only includes positive numbers

In the example function y = cube root of (x - 2), what is the range of x-values considered?

• -10 to 6

• -6 to 10

• 0 to 10

• -10 to 0

Why do we focus on integer values when creating a table of values for graphing?

• Integers avoid the need to estimate decimal points

• Integers are the only values that can be graphed

• Integers provide a more accurate graph

• Integers are easier to calculate

What is the cube root of -8?

• -2

• 4

• -4

• 2

How do you find the y-value for a given x-value in the function y = cube root of (x - 2)?

• Divide x by 2 and find the square root

• Add 2 to x and find the square root

• Subtract 2 from x and find the cube root

• Multiply x by 2 and find the cube root

What is the purpose of using a graphing calculator in this context?

• To quickly find y-values for various x-values

• To determine the maximum and minimum points

• To calculate the area under the curve

• To find the derivative of the function

What is the first step in plotting the graph of a cube root function?

• Calculate the derivative of the function

• Find the maximum and minimum points

• Plot the points on the graph

• Draw a straight line through the points

What common mistake do students make when connecting points on a cube root graph?

• Using curved lines

• Using straight lines

• Plotting too many points

• Ignoring the domain

Why should arrows not be included at the endpoints of a graph with a restricted domain?

• Arrows indicate the graph continues beyond the domain

• Arrows are only used for linear functions

• Arrows make the graph look incomplete

• Arrows are unnecessary for cube root functions

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

• A straight line

• A circle

• A parabola

• A curved line