Analyzing Graphs of Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, meaning it has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, meaning its rate of change varies.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean for a graph to be increasing?

Back

A graph is increasing when the y-values rise as the x-values increase.

Front

What does it mean for a graph to be decreasing?

Back

A graph is decreasing when the y-values fall as the x-values increase.

Front

What does it mean for a graph to be constant?

Back

A graph is constant when the y-values remain the same as the x-values change.

Front

What is the significance of the slope in a linear function?

Back

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

Front

What is a distance-time graph?

Back

A distance-time graph shows the distance traveled by an object over time, illustrating its speed and direction.

Front

What does a flat line on a distance-time graph represent?

Back

A flat line represents that the object is not moving; the distance remains constant over time.