Lesson 3.3: Compare Linear and Non-Linear Functions

Lesson 3.3

Compare Linear and Non Linear Functions​

By Reed Carbone

Definition:

​Constant Rate of Change: The constant rate of change is present in linear functions. It is the ratio of vertical change to horizontal change. Hmm where have we heard this before...

Initial Value: The initial value is where your linear function starts. In terms of coordinates, it is whatever your y value is when your x value is 0.

Slope Intercept Form: y = mx + b where m is the slope and b is the y intercept.​

​Linear vs. Non Linear Functions

Multiple Choice

Is the function linear or non linear?

• Linear

• Non Linear

• Yes

• No

Multiple Choice

Determine whether the functions are linear or non linear.

• Function I: NonLinear

  Function II: NonLinear

• Function I: Linear

  Function II: Linear

• Function I: Linear

  Function II: NonLinear

• Function I: NonLinear

  Function II: Linear

​How to identify the constant rate of change and initial value in different linear Functions:

​Graphs:

Constant Rate of Change:

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Initial Value:

​How to identify the constant rate of change and initial value in different linear Functions:

​Equations:

Constant Rate of Change:

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.

.

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Initial Value:

​y = -4x + 5

​How to identify the constant rate of change and initial value in different linear Functions:

​Table:

Constant Rate of Change:

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.

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Initial Value:

​What is the constant rate of change in the function?

Multiple Choice

What is the constant rate of change in the function?

• 4

• 3

• 2

• 1

​Compare the equation and the graph, which had a greater constant rate of change? y = -2x + 4

​Two functions are shown below, which has a greater constand rate of change?

Multiple Choice

Two functions are shown below, which has a greater constant rate of change

• Function 1

• Function 2

• Function 3

• Function 4

​Two functions are shown. Find the constant rate of change and initial value for both and compare:

Multiple Choice

Compare the constant rate of change for all functions. Which is greater?

• y = x + 1

​Conclusion: Write two complete sentences about what you learned.