Linear or 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 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 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 line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x). It is represented by the letter m in the equation of a line.

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. It represents the value of y when x is 0.

Front

Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line. This indicates that the output value (y) remains constant regardless of the input value (x).

Front

What is an example of a nonlinear function?

Back

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

Front

How do you determine if an equation is linear or nonlinear?

Back

To determine if an equation is linear, check if it can be rearranged into the form Ax + By = C. If it cannot, it is likely nonlinear.

Front

What is the difference between a linear function and a nonlinear function in terms of graph shape?

Back

A linear function produces a straight line graph, while a nonlinear function produces a curve or a more complex shape.