Review Flashcard 1

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for the second finite difference to be constant?

Back

If the second finite difference is constant, it indicates that the function is quadratic. This means that the differences of the differences of the function's values are the same.

Front

How do you predict values using finite differences?

Back

To predict values using finite differences, calculate the first differences, then the second differences, and continue until a pattern emerges. Use this pattern to extrapolate future values.

Front

What characterizes an exponential function?

Back

An exponential function is characterized by a constant ratio between consecutive terms, typically in the form f(x) = ab^x, where a is a constant and b is the base.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant factor, leading to much faster growth over time.

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree 3, typically in the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

How can you identify an exponential relationship from a table of values?

Back

An exponential relationship can be identified if the ratio of consecutive values is constant or if the differences of the logarithms of the values are constant.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of the function when x = 0.

Front

What does it mean for a function to model population growth?

Back

A function that models population growth typically reflects how the population changes over time, often using exponential functions to represent rapid growth.