Patterns and NonLinear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, and its rate of change is not constant.

Front

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

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.

Front

What does a constant rate of change mean?

Back

A constant rate of change means that for every unit increase in x, the change in y is always the same.

Front

What is the slope of a linear function?

Back

The slope is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the significance of the y-intercept in a linear function?

Back

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

Front

How do you determine if a function is nonlinear from a graph?

Back

If the graph curves or does not form a straight line, the function is nonlinear.

Front

What is an example of a nonlinear function?

Back

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

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.

Front

What does it mean if a function has no constant slope?

Back

It means the function is nonlinear, as the rate of change varies at different points.