Analyzing Functions and Graphs

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What defines a function in mathematics?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

What does a distance vs time graph represent?

Back

It shows how distance changes over time for an object in motion.

Front

What indicates a steady pace on a distance vs time graph?

Back

A straight, diagonal line indicates a steady pace, while a horizontal line indicates no movement.

Front

How can you tell if two runners ran for the same amount of time on a distance vs time graph?

Back

If the graphs of both runners end at the same time on the time axis.

Front

What does it mean if a graph crosses the x-axis?

Back

It indicates that the output (y-value) is zero at that point.

Front

What is the significance of the slope in a distance vs time graph?

Back

The slope represents the speed of the runner; a steeper slope indicates a faster speed.

Front

What does a horizontal line on a distance vs time graph indicate?

Back

It indicates that the object is at rest and not changing its distance over time.

Front

What is a relation in mathematics?

Back

A set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a relation is a function from a set of ordered pairs?

Back

Check if any x-value is repeated with different y-values; if so, it is not a function.