Linear or 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 can be represented by equations such as y = ax^2, y = ax^3, etc.

Front

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

Back

A linear function will have a constant rate of change between the x-values and y-values. This means that the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What does it mean if a function is described as 'nonlinear'?

Back

If a function is described as 'nonlinear', it means that the relationship between the variables does not follow a straight line, indicating that the rate of change varies.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation has a constant rate of change and can be represented as a straight line, while a nonlinear equation has a variable rate of change and cannot be represented as a straight line.

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 and the output (y-value) remains constant regardless of the input (x-value).

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

Front

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

Back

If the graph of the function is a straight line, it is linear. If the graph curves or has bends, it is nonlinear.