Linear and Non-Linear Functions

Front

What is a linear function?

Back

A linear function is a function that has a constant rate of change, represented by a straight line on a graph.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change, resulting in a curved line on a graph.

Front

What does it mean for a function to have a constant rate of change?

Back

It means that for every unit increase in the input (x), the output (y) increases by a fixed amount.

Front

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

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the function is linear.

Front

What is the definition of a function?

Back

A function is a relation where every input has exactly one output.

Front

What is the slope of a linear function?

Back

The slope is the measure of the steepness of the line, calculated as the change in y divided by the change in x.

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 as (0, 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you tell if a graph is linear or nonlinear?

Back

A graph is linear if it forms a straight line; it is nonlinear if it curves.

Front

What is an example of a nonlinear function?

Back

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