Writing and interpreting functions

Front

What does the average rate of change represent in a function?

Back

The average rate of change represents the change in the output value (y) divided by the change in the input value (x) over a specified interval.

Front

How do you calculate the average rate of change of a function over an interval [a, b]?

Back

The average rate of change is calculated using the formula: (f(b) - f(a)) / (b - a).

Front

What is the average rate of change of the function g(x) = x^2 + 1 over the interval [-5, -2]?

Back

The average rate of change is -7.

Front

What does a positive rate of change indicate about a function's graph?

Back

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

Front

What does a negative rate of change indicate about a function's graph?

Back

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

Front

What is the formula for average rate of change?

Back

The formula for average rate of change is: change in y / change in x.

Front

In the context of a graph, what does the slope represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

If a car travels 32 miles per gallon of gasoline, what is the rate of change in terms of distance per gallon?

Back

The rate of change is 32 miles per gallon.

Front

What is the significance of the average rate of change in real-world applications?

Back

The average rate of change helps to understand how one quantity changes in relation to another, which is crucial in fields like physics, economics, and biology.

Front

How can you interpret the average rate of change from a table of values?

Back

You can interpret the average rate of change by calculating the difference in the output values (y) and dividing it by the difference in the input values (x) for the given intervals.