Identifying Linear 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 graph can be curved or have various shapes.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph. If the graph is not straight, it is not a linear function.

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 y changes for a unit change in x.

Front

What is the y-intercept 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 the value of b in the equation y = mx + b.

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 and does not change in value as x changes.

Front

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

Back

A linear equation can be written in the form y = mx + b, while a nonlinear equation cannot be expressed in this form and may include exponents, roots, or other operations.

Front

What is an example of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

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

Front

How do you determine if a function is linear or nonlinear from a table of values?

Back

If the differences between consecutive y-values are constant for equal changes in x-values, the function is linear. If the differences vary, it is nonlinear.