Average Rate of Change / Functions and their Graphs

Front

What is the average rate of change?

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 x=a to x=b?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a)

Front

What does it mean if the average rate of change is positive?

Back

It means that the function is increasing over the interval from a to b.

Front

What does it mean if the average rate of change is negative?

Back

It means that the function is decreasing over the interval from a to b.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) that the function can produce.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is a graph of a function?

Back

A graph of a function is a visual representation of the relationship between the input values and the output values.

Front

What does it mean for a function to be constant?

Back

A constant function is one where the output value does not change regardless of the input value.