Linear vs NonLinear Functions

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 graph can be a curve or any shape that is not a straight line.

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 the y-intercept represent in a linear function?

Back

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

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change; the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Front

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

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How can you tell if a function is linear from its equation?

Back

If the equation can be rearranged to the form y = mx + b, it is linear. If it includes variables multiplied together or raised to a power, it is nonlinear.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.