Linear or Nonlinear Function

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 varying slopes.

Front

Identify the general form of a linear function.

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0; it is the point where the line crosses the y-axis.

Front

How can you determine if a function is linear from its equation?

Back

If the equation can be expressed in the form y = mx + b, it is linear. If it includes variables raised to powers other than 1, it is nonlinear.

Front

What is the graph of a linear function?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What is the graph of a nonlinear function?

Back

The graph of a nonlinear function can be curved, parabolic, or have other shapes that are not straight lines.

Front

Give an example of a linear function.

Back

An example of a linear function is y = 3x + 2.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is y = x^2 + 1.