Linear vs. Nonlinear 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 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 graph can be curved or have varying slopes.

Front

Which equation represents a linear function? y = 3x + 2 or y = x^2?

Back

y = 3x + 2 represents a linear function.

Front

What is the slope in the equation y = 5x - 1?

Back

The slope is 5.

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, represented by the value of b in the equation y = mx + b.

Front

How can you determine if a function is linear from a table of values?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the function is 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

Is the function represented by the graph a linear function if it has a constant slope?

Back

Yes, if the graph has a constant slope, it is a linear function.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2 or y = sin(x).

Front

How do you identify a linear function from a graph?

Back

A linear function will show a straight line, while a nonlinear function will show curves or bends.