Linear vs NonLinear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its graph can be a curve or any shape that is not a straight line.

Front

What is the general form of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically expressed in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the general form of a cubic function?

Back

A cubic function is a polynomial function of degree 3, typically expressed in the form y = ax³ + bx² + cx + d, where a, b, c, and d are constants.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the difference between linear and nonlinear functions in terms of their graphs?

Back

Linear functions graph as straight lines, while nonlinear functions graph as curves or other shapes.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear function?

Back

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

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is a square root function?

Back

A square root function is a function of the form y = √x, which graphs as half of a parabola opening to the right.