Analyzing Graphs of Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

What does the slope of a graph represent?

Back

The slope of a graph represents the rate of change of the function. It indicates how much the output (y-value) changes for a given change in the input (x-value).

Front

How can you determine if a graph is increasing or decreasing?

Back

A graph is increasing if the y-values rise as the x-values increase, and it is decreasing if the y-values fall as the x-values increase.

Front

What does a horizontal line on a graph indicate?

Back

A horizontal line indicates that the output (y-value) remains constant regardless of the input (x-value), meaning the function has a slope of zero.

Front

What does a vertical line on a graph indicate?

Back

A vertical line indicates that for a given x-value, there are multiple y-values, which means it does not represent a function.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. It represents the output value when the input is zero.

Front

How do you find the distance covered in a specific time interval on a graph?

Back

To find the distance covered in a specific time interval, look at the change in the y-values (distance) between the two corresponding x-values (time) on the graph.

Front

What does it mean if a graph is stationary?

Back

A stationary graph means that the output (y-value) does not change as the input (x-value) changes, indicating no movement or change in distance.

Front

How can you identify the fastest runner from a graph?

Back

The fastest runner can be identified by the steepest slope on the graph, which indicates the greatest rate of change in distance over time.

Front

What does it mean if a graph shows a steep slope?

Back

A steep slope indicates a rapid change in the output (y-value) for a small change in the input (x-value), suggesting a high speed or rate.