Linear vs Nonlinear

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, exponential, or logarithmic.

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

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

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 corresponding y-values in a table.

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines, while nonlinear graphs can be curves or other shapes, indicating varying rates of change.

Front

What is an example of a nonlinear function?

Back

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

Front

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

Back

If the equation can be rearranged to the form y = mx + b, it is linear; otherwise, it is nonlinear.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.