Recognizing Patterns in Nonlinear Functions

The video tutorial introduces nonlinear functions and explains how to identify their patterns. It contrasts linear and nonlinear functions, highlighting the constant rate of change in linear functions. The tutorial demonstrates finding common differences in sequences and explains how these differences relate to the degree of the function. It covers graphing quadratic and cubic functions, discussing their domains and ranges. The video concludes with an exploration of cubic functions and cube patterns, using a table to illustrate the relationship between the number of blocks per edge and the total number of blocks in a cube.

What is a key characteristic of a linear function?

• It is always decreasing.

• It has a variable rate of change.

• It forms a curve on a graph.

• It has a constant rate of change.

How do you find a common difference in a table of values for a linear function?

• By adding consecutive terms.

• By multiplying consecutive terms.

• By subtracting consecutive terms.

• By dividing consecutive terms.

What pattern is identified when the second difference in a table is constant?

• Linear pattern

• Quadratic pattern

• Cubic pattern

• Exponential pattern

What is the rule for a cubic function based on the pattern of differences?

• y = x + 3

• y = x^2

• y = x^3

• y = 3x

What is a common misunderstanding when calculating differences in tables?

• Subtracting preceding terms

• Adding preceding terms

• Subtracting succeeding terms

• Multiplying succeeding terms

In the context of cubes, what does the variable 'E' represent?

• The number of blocks per edge

• The volume of the cube

• The total number of blocks

• The surface area of the cube

Why is a discrete graph used for the cubic function in the cube example?

• Because the function is continuous

• Because the function is quadratic

• Because the function is linear

• Because only whole blocks are used