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

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 over run (change in y over change in x).

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 y when x is 0.

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 in the table.

Front

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

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph can be curved or have varying slopes.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How do you determine if a function is linear or nonlinear from its equation?

Back

If the equation can be rearranged to the form y = mx + b, it is linear. If it contains variables raised to powers greater than one or products of variables, it is nonlinear.

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function indicates the highest power of the variable, which affects the function's shape and behavior.