Comparing Linear and 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 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 rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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 any two points.

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). It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the value of the function when x = 0.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which indicates that as x increases, y decreases.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (e.g., f(x) = x^2), exponential functions (e.g., f(x) = 2^x), and trigonometric functions (e.g., f(x) = sin(x)).

Front

How can 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.

Front

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

Back

The coefficients in a linear function determine the slope and the y-intercept, which affect the position and steepness of the line on the graph.