Linear vs. Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in 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 be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values. If the differences are not constant, the function is nonlinear.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means that as the x-value increases, the y-value decreases.

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 are some examples of linear functions?

Back

Examples of linear functions include y = 2x + 3, y = -x + 5, and y = 0.5x - 1.

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include y = x^2, y = √x, and y = sin(x).

Front

How can you tell if an equation is linear?

Back

An equation is linear if it can be rearranged into the form y = mx + b, where m and b are constants, and it does not contain variables raised to a power greater than one.