Identifying Linear and Nonlinear Functions

The lesson explains how to distinguish between linear and nonlinear functions using tables, equations, and graphs. It covers the concept of constant rate of change for linear functions and how nonlinear functions differ. Examples are provided to illustrate these concepts, including graphing interest accounts to compare linear and nonlinear growth. The lesson concludes with a practice section for identifying linear and nonlinear functions.

What is a key characteristic of a linear function?

• It forms a curve on a graph.

• It cannot be represented in a table.

• It has a constant rate of change.

• It has a variable rate of change.

In Example 1, what indicates that a table is linear?

• The X values increase by different amounts.

• The Y values decrease by different amounts.

• Both X and Y values show a constant pattern.

• The table has more than two columns.

Why is letter B in Example 2 considered nonlinear?

• It forms a straight line on a graph.

• It can be written as y = MX + B.

• It has a variable in the denominator.

• It has a variable in the numerator.

How can you visually identify a linear function on a graph?

• It forms a circle.

• It forms a zigzag pattern.

• It forms a straight line.

• It forms a spiral.

What does the graph of Account A indicate about its balance over time?

• The balance decreases over time.

• The balance remains constant.

• The balance fluctuates randomly.

• The balance increases linearly.

What happens to Account B's balance after year 2?

• It starts to curve upwards.

• It remains constant.

• It decreases sharply.

• It forms a straight line.

In the practice section, why is the second example considered nonlinear?

• It is made up of two continuous lines.

• It has no variables.

• It is made up of two separate lines.

• It forms a perfect circle.

What is not allowed in a linear function's equation?

• Variables in the numerator.

• Variables in the denominator.

• Linear coefficients.

• Constant terms.

What makes a function nonlinear according to the practice section?

• Having constant coefficients.

• Having exponents.

• Having no variables.

• Being a straight line.

What is the main focus of the practice section?

• Identifying linearity in graphs.

• Identifying linearity in equations.

• Identifying linearity in various forms.

• Identifying linearity in tables.