Linear and 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 f(x) = 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, exponential, or logarithmic.

Front

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

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

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). It indicates how much y changes for a unit change in x.

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. It represents the value of the function when x = 0.

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

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as x increases, y decreases.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola when graphed.

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 bends, the function is nonlinear.

Front

What is the difference between a linear function and a linear equation?

Back

A linear function describes a relationship between variables, while a linear equation is a mathematical statement that asserts the equality of two expressions.