AP Precalculus 1.1-1.3

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 a table of values?

Back

To calculate the average rate of change from a table, subtract the function value at the beginning of the interval from the function value at the end of the interval, then divide by the difference in the input values.

Front

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

Back

If the average rate of change is decreasing, it means that the function's output is increasing at a slower rate over the specified interval.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by a constant rate of change.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically represented in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How can you determine if a function is linear or quadratic from a table of values?

Back

A function is linear if the differences between consecutive outputs are constant; it is quadratic if the differences of the differences (second differences) are constant.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function represents the rate of change of the function, indicating how much the output changes for a unit change in the input.

Front

What does it mean for a graph to have a decreasing rate of growth?

Back

A graph with a decreasing rate of growth shows that while the output is still increasing, it is doing so at a slower pace over time.

Front

What is the relationship between a function's rate of change and its graph?

Back

The rate of change of a function can be observed in its graph: a steeper slope indicates a higher rate of change, while a flatter slope indicates a lower rate of change.

Front

How do you interpret a graph that shows population growth?

Back

A graph showing population growth typically indicates how the population size changes over time, with the slope representing the growth rate.