Linear vs Non-linear

Front

What is the definition of a linear function?

Back

A linear function is a function whose graph is a straight line.

Front

What characterizes a nonlinear function?

Back

A nonlinear function is characterized by a graph that is not a straight line, which may include curves, bends, or other shapes.

Front

How can you determine if a graph represents a linear relationship?

Back

A graph represents a linear relationship if it forms a straight line when plotted.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is a quadratic function, such as y = x^2, which produces a parabolic graph.

Front

How can you identify a nonlinear relationship from a table of values?

Back

A nonlinear relationship can be identified from a table of values if the differences between consecutive y-values do not form a constant pattern.

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.