Analyzing Graphs

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values (x) increase, the output values (y) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values (x) increase, the output values (y) decrease.

Front

What is a constant function?

Back

A constant function is one where the output value (y) remains the same regardless of the input value (x).

Front

How can you identify increasing intervals on a graph?

Back

Increasing intervals can be identified where the graph slopes upwards from left to right.

Front

How can you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified where the graph slopes downwards from left to right.

Front

What does it mean for a function to be linear?

Back

A linear function is one that graphs as a straight line, indicating a constant rate of change.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is one that does not graph as a straight line, indicating a variable rate of change.

Front

What is the significance of the slope of a line on a graph?

Back

The slope indicates the rate of change of the function; a positive slope means increasing, while a negative slope means decreasing.

Front

What is an interval in the context of a graph?

Back

An interval is a range of x-values over which a function is analyzed.

Front

How do you determine if a function is never decreasing?

Back

A function is never decreasing if it either increases or remains constant over its entire domain.