Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in 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. It can have varying rates of change and can include curves, parabolas, and other shapes.

Front

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

Back

A linear function will have a constant difference in the y-values for equal increments in the x-values. If the differences vary, the function is nonlinear.

Front

What does it mean for a function to be 'never increasing'?

Back

A function that is 'never increasing' means that as the x-values increase, the y-values do not increase; they either decrease or remain constant.

Front

What does it mean for a function to be 'never decreasing'?

Back

A function that is 'never decreasing' means that as the x-values increase, the y-values do not decrease; they either increase or remain constant.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by 'b' in the equation y = mx + b.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-values increase, the y-values decrease.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola and does not form a straight line.

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 can be curved or have varying slopes, indicating changing rates of change.