Analyzing Function Graphs

Front

What does it mean for a function to be 'never decreasing'?

Back

A function is 'never decreasing' if its value does not decrease as the input increases. This means that as you move from left to right on the graph, the function either stays the same or increases.

Front

What is the significance of a graph showing a flat line?

Back

A flat line on a graph indicates that the object is moving at a constant speed, meaning there is no change in position over time.

Front

What does it mean when a graph is increasing?

Back

When a graph is increasing, it means that as the x-values increase, the y-values also increase. This indicates that the object is gaining speed.

Front

What does it mean when a graph is decreasing?

Back

When a graph is decreasing, it means that as the x-values increase, the y-values decrease. This indicates that the object is losing speed.

Front

What does acceleration mean in the context of a graph?

Back

Acceleration refers to the rate of change of velocity. In a graph, it is represented by a curve that slopes upwards.

Front

What does it mean for an object to be 'not moving' in a graph?

Back

An object is 'not moving' when the graph is flat (horizontal line), indicating that there is no change in position over time.

Front

How can you tell if an object is slowing down from a graph?

Back

An object is slowing down if the graph shows a decreasing slope, meaning the y-values are increasing at a slower rate as the x-values increase.

Front

What does it mean for a graph to represent someone who speeds up and then slows down?

Back

This graph will show an initial upward slope (speeding up) followed by a downward slope (slowing down), indicating changes in speed over time.

Front

What is the importance of intervals in analyzing function graphs?

Back

Intervals help identify specific sections of the graph where the function behaves in a certain way, such as increasing, decreasing, or remaining constant.

Front

What does a steep slope on a graph indicate?

Back

A steep slope indicates a rapid change in position, meaning the object is moving quickly.