Identifying Non-Linear Function Patterns

The video tutorial covers patterns and nonlinear functions, focusing on identifying and representing these patterns. It begins with definitions and examples of linear and nonlinear functions. The tutorial includes three examples: analyzing graphs of pizza area and sauce cost to determine linearity, using patterns to represent relationships with blocks and cubes, and finding equations for nonlinear functions from ordered pairs. The video emphasizes using various representations like words, tables, equations, and graphs to understand these functions.

What is a linear function?

• A function represented only by a vertical line

• A function that cannot be graphed

• A function whose graph is a non-vertical line

• A function represented by a curve

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which of the following is an example of a nonlinear function?

• Parabola

• Diagonal line

• Horizontal line

• All of the above

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CCSS.8.F.A.3

Is the function describing the area of a pizza based on its radius linear or nonlinear?

• Linear

• Cannot be determined

• Nonlinear

• None of the above

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CCSS.8.F.A.3

What does a uniform increase in a table suggest about a function?

• The function is not a function

• The function is nonlinear

• The function is undefined

• The function is linear

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CCSS.8.F.A.3

What is the primary method used to determine if a function is linear or nonlinear in the examples given?

• None of the above

• Graphical representation

• Asking an expert

• Using a calculator

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CCSS.8.F.A.3

How is the total number of blocks calculated when given the number of blocks on one edge?

• Dividing the number of blocks by three

• None of the above

• Adding the blocks

• Multiplying the number of blocks by itself three times

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CCSS.8.EE.A.2

What pattern is observed in the table of blocks and edges?

• Additive increase

• Cubic increase

• Exponential decrease

• Linear increase

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CCSS.6.EE.B.6

Which equation correctly represents the function based on the ordered pairs given?

• y = x^2

• y = 2^x

• y = x + 1

• y = 2x

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What does the equation 'y = 2^x' suggest about the function's growth?

• No growth

• Cubic growth

• Exponential growth

• Linear growth

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CCSS.HSF-IF.C.8B

How can you verify the correctness of a function's equation using a table?

• None of the above

• By drawing the graph only

• By guessing and checking

• By checking if the outputs match for all inputs

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CCSS.8.EE.C.8B