Linear or NonLinear Flashcard

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, cubic, or exponential.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input (x) increases, the output (y) decreases.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph can be curved, indicating a variable rate of change.

Front

What is a cubic function?

Back

A cubic function is a nonlinear function that can be expressed in the form y = ax³ + bx² + cx + d, where a, b, c, and d are constants.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.