Linear/Nonlinear

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, 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 does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear function?

Back

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

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 an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a quadratic function and forms a parabola when graphed.

Front

How can you tell if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test, meaning that no vertical line intersects the graph at more than one point.

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 is curved or has bends, indicating a variable rate of change.

Front

What is a common characteristic of nonlinear functions?

Back

Nonlinear functions often have varying slopes and can exhibit behaviors such as curvature, oscillation, or exponential growth.