Linear vs Nonlinear Functions Flashcards

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Questions and Answers

Which of these statements is true regarding Leslie's conclusion about the function?

Leslie's conclusion is wrong. (correct)

The rate of change is constant.

Leslie's conclusion is correct.

The function is linear.

What is the rate of change of the function represented by the table?

What mistake did Willis make in his analysis of the table?

He did not calculate any differences.

He thought the function has a constant rate of change. (correct)

He miscalculated the differences.

He concluded the function is non-linear.

Which of these tables represents a linear function?

B Signup and view all the answers

Is the function represented by the table linear?

False Signup and view all the answers

What is the rate of change for Carol's skiing distance?

3/16 Signup and view all the answers

Which graph has a rate of change of zero?

Graph B Signup and view all the answers

Which graph represents a function with a rate of change of 0.5?

Graph D Signup and view all the answers

What is the rate of change of the function?

-2 Signup and view all the answers

What was Kevin's mistake while finding the rate of change?

He mixed up the numerator and the denominator of the fraction. Signup and view all the answers

What is the conclusion about Jordana's function regarding its linearity?

It is not linear because it does not have a constant rate of change. Signup and view all the answers

What is the rate of change of the function represented by the table?

2.5 Signup and view all the answers

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)?

-5 Signup and view all the answers

What is the rate of change between point A and point B in the graph of the linear function?

2 Signup and view all the answers

What explains whether or not Jamal's function is linear?

It is linear because it has a constant rate of change. Signup and view all the answers

Does the situation with the number of math problems Jana completed represent a linear function?

False Signup and view all the answers

Which of these tables represents a non-linear function?

C Signup and view all the answers

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.

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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.