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, a circle, or any other 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

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 y-intercept of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

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

Front

How do you determine if a function is linear or nonlinear from its graph?

Back

If the graph is a straight line, the function is linear. If the graph curves or has any bends, it is nonlinear.

Front

What does it mean for a function to be quadratic?

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.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).