Linear vs Non-Linear

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 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. Its rate of change is not constant, and it can take various forms such as quadratic, cubic, or exponential.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if it forms a straight line. The slope is constant, and there are no curves or bends.

Front

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

Back

A nonlinear function can be identified from a table of values if the differences between the y-values do not change consistently as the x-values increase.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise/run).

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. It represents the value of y when x is 0.

Front

Which of the following equations is linear: y = 2x + 3 or y = x^2?

Back

y = 2x + 3 is a linear equation because it can be represented as a straight line. y = x^2 is nonlinear.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

Can a vertical line be considered a linear function?

Back

No, a vertical line cannot be considered a linear function because it does not pass the vertical line test; it does not have a unique y-value for each x-value.

Front

What is the difference between a linear and a quadratic function?

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.