Identifying 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 graph can be a curve, a circle, or any other shape that is not a straight line.

Front

How can you identify a linear function from its equation?

Back

If the equation can be written in the form y = mx + b, where m and b are constants, it is a linear function.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of the function, represented by 'm' in the equation y = mx + b. It indicates how steep the line is.

Front

What does the y-intercept represent in a linear function?

Back

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

Front

Give an example of a linear function.

Back

An example of a linear function is f(x) = 2x + 3.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is f(x) = x^2 + 2.

Front

What is the graph of a linear function like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What is the graph of a nonlinear function like?

Back

The graph of a nonlinear function can be curved, circular, or take on various shapes that are not straight lines.

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.