Describing the Behavior of Linear and Nonlinear Graphs

This lesson covers how to describe the rate of change in linear and nonlinear functions by analyzing graphs. It explains the differences between increasing and decreasing rates, constant rates, and how to identify these behaviors in functions. The lesson also provides examples to illustrate these concepts, focusing on how functions behave over different intervals.

What is the correct formula for calculating the slope of a line?

• Change in x divided by change in y

• Change in y divided by change in x

• Sum of x and y

• Difference between x and y

How do you describe a function that increases by larger amounts as x increases?

• Increasing at a decreasing rate

• Decreasing at an increasing rate

• Increasing at an increasing rate

• Increasing at a constant rate

What does it mean when a function is increasing at a constant rate?

• The y values increase by the same amount for each increase in x

• The y values decrease by the same amount for each increase in x

• The y values increase by larger amounts for each increase in x

• The y values decrease by larger amounts for each increase in x

Which of the following describes a function that is decreasing at a decreasing rate?

• The y values increase by smaller amounts as x increases

• The y values increase by larger amounts as x increases

• The y values decrease by smaller amounts as x increases

• The y values decrease by larger amounts as x increases

What happens to the ratio of change in y to change in x when a function is decreasing at an increasing rate?

• The ratio increases

• The ratio becomes zero

• The ratio decreases

• The ratio remains constant

In the example provided, what is the behavior of the function from negative infinity to 0?

• Increasing at a constant rate

• Increasing at a decreasing rate

• Decreasing at a constant rate

• Decreasing at an increasing rate

From 1 to positive infinity, how is the function described in the example?

• Decreasing at a constant rate

• Increasing at a constant rate

• Increasing at an increasing rate

• Decreasing at an increasing rate