Linear and Non-Linear Functions

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 f(x) = 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 graph can be a curve or any other shape that is not linear.

Front

What is the slope of a line?

Back

The slope of a line 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 function?

Back

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

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by its straight-line graph. If the graph curves or bends, it is not linear.

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 an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a slope of 2 and a y-intercept of 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which forms a parabola when graphed.

Front

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

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear. If not, it is nonlinear.

Front

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

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve or other shapes.