Key Features of Graphs and Average Rate of Change

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 find the x-intercept of a graph?

Back

To find the x-intercept, set the output (y) of the function to zero and solve for the input (x).

Front

What does it mean for a graph to have a minimum?

Back

A minimum of a graph is a point where the function value is lower than all nearby points, indicating a local low point.

Front

What is the domain of a function?

Back

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

Front

What is an increasing interval on a graph?

Back

An increasing interval is a range of x-values where the function's output (y-value) is rising as x increases.

Front

How do you determine the minimum number of minima on a graph?

Back

To determine the minimum number of minima, analyze the graph's turning points where the slope changes from negative to positive.

Front

What is the significance of the initial fee in a car rental model?

Back

The initial fee represents a fixed cost that is charged regardless of the distance driven.

Front

How do you calculate the average rate of change between two points?

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 is an x-intercept?

Back

An x-intercept is a point where the graph crosses the x-axis, meaning the output (y) is zero.

Front

What does it mean for a graph to have all real numbers as its domain?

Back

It means that the function is defined for every possible x-value without any restrictions.