Questions and Answers
Which of these statements is true regarding Leslie's conclusion about the function?
What is the rate of change of the function represented by the table?
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What mistake did Willis make in his analysis of the table?
Which of these tables represents a linear function?
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Is the function represented by the table linear?
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What is the rate of change for Carol's skiing distance?
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Which graph has a rate of change of zero?
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Which graph represents a function with a rate of change of 0.5?
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What is the rate of change of the function?
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What was Kevin's mistake while finding the rate of change?
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What is the conclusion about Jordana's function regarding its linearity?
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What is the rate of change of the function represented by the table?
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If the rate of change between the points (-5, 10) and (-4, 5) is -5, what is the rate of change between the points (-3, 0) and (-2, -5)?
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What is the rate of change between point A and point B in the graph of the linear function?
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What explains whether or not Jamal's function is linear?
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Does the situation with the number of math problems Jana completed represent a linear function?
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Which of these tables represents a non-linear function?
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Study Notes
Linear vs. Nonlinear Functions
- A function is non-linear if the rate of change between points is not constant.
- Leslie incorrectly concluded that a function with non-constant rate of change is linear.
- The rate of change for a table representing a function can be evaluated by finding differences in y-values.
Key Mistakes in Function Analysis
- Willis made an error by concluding a function has a constant rate of change based on increasing differences in y-values.
- Carol's skiing distance changed at a rate of 3/16.
- Kevin's error in calculating rate of change was due to mixing up the numerator and denominator.
Graph Interpretations
- Graph B has a rate of change of zero.
- Graph D represents a function with a rate of change of 0.5.
Rate of Change Calculations
- The rate of change between the points (-5, 10) and (-4, 5) is -5, same as between (-3, 0) and (-2, -5).
- The rate of change between points A and B in a linear graph is 2, which remains consistent between points C and D as well.
Functions and Rates of Change
- A function represented by a table that does not have a constant rate of change is identified as non-linear.
- The situation presented by the math problems Jana completed as time progresses is non-linear due to lack of a constant rate of change.
Tables Representing Functions
- Table B represents a linear function.
- Table C represents a non-linear function.
Studying That Suits You
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Description
Test your understanding of linear and nonlinear functions with these flashcards. Analyze graphs and determine the rate of change between points to classify the functions. Perfect for students looking to reinforce their knowledge in this area.
