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 determine if a function is linear or nonlinear from a table of values?

Back

If the ratio of the change in y to the change in x is constant for all intervals, the function is linear. If this ratio changes, the function is nonlinear.

Front

What is the equation of a linear function?

Back

An example of a linear function is y = 8x, which represents a straight line with a slope of 8.

Front

What is the equation of a nonlinear function?

Back

An example of a nonlinear function is y = 4x^2, which represents a parabola.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

Is the function y = \frac{8}{x^2} linear or nonlinear?

Back

Nonlinear, because it does not form a straight line and the relationship between x and y is not constant.

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 linear function?

Back

A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between x and y.