Rate of Change (Graphs, Tables and Word Problems))

Front

What is the average rate of change in a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change from a table of values?

Back

To calculate the average rate of change from a table, subtract the initial value from the final value and divide by the difference in the corresponding input values.

Front

What is the formula for average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where f(b) and f(a) are the function values at points b and a.

Front

What does a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

How can you interpret the slope of a graph in terms of rate of change?

Back

The slope of a graph represents the rate of change; a steeper slope indicates a greater rate of change.

Front

What is the average rate of change for a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Front

How do you find the average rate of change from a graph?

Back

To find the average rate of change from a graph, identify two points on the graph, determine their coordinates, and apply the average rate of change formula.

Front

What is the significance of the units in average rate of change?

Back

The units in average rate of change provide context for the change being measured, such as dollars per hour or feet per minute.

Front

How does the average rate of change relate to real-world problems?

Back

The average rate of change can be used to analyze trends in real-world situations, such as speed, cost, or growth rates.