Linear versus 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. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation f(x) = mx + b. It is calculated as the change in y divided by the 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 is represented by 'b' in the equation f(x) = mx + b.

Front

Give an example of a linear function.

Back

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

Front

Give an example of a nonlinear function.

Back

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

Front

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

Back

A linear equation represents a straight line and has a constant rate of change, while a nonlinear equation represents a curve and has a variable rate of change.

Front

How do 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 bends, it is nonlinear.

Front

What is the general form of a linear equation in two variables?

Back

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