Analyzing Graphs of Functions

Front

What does it mean for a function to decrease at a constant rate?

Back

It means that the function's output decreases by the same amount for each unit increase in the input, resulting in a straight line with a negative slope on a graph.

Front

How can you determine which person is running the fastest from a graph?

Back

You can determine the fastest runner by comparing the steepness of their lines on the graph; the steeper the line, the faster the speed.

Front

What does a horizontal line on a graph represent?

Back

A horizontal line represents a constant speed, indicating that the object is moving at the same rate over time.

Front

What does a vertical line on a graph indicate?

Back

A vertical line indicates that the object is not moving, as the input (time) does not change while the output (distance) does.

Front

How do you find the point where one object passes another on a graph?

Back

You find the point where the lines representing the two objects intersect; this point indicates the distance at which one object overtakes the other.

Front

What does the slope of a line on a graph represent?

Back

The slope represents the rate of change of the function; a positive slope indicates an increase, while a negative slope indicates a decrease.

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, representing the value of the function when the input is zero.

Front

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

Back

If the line on the graph curves upwards, it indicates that the object is accelerating; a straight line indicates constant speed.

Front

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

Back

A steep line indicates a high rate of change, meaning the function is increasing or decreasing rapidly.

Front

How do you interpret the area under a curve on a graph?

Back

The area under the curve can represent total distance traveled over time, depending on the context of the graph.