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 graph can be curved or have varying slopes.

Front

How can you identify a linear function from its equation?

Back

If the equation can be expressed in the form y = mx + b, it is a linear function. If it includes variables raised to a power greater than one, it is nonlinear.

Front

What is the slope of a linear function?

Back

The slope (m) of a linear function represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

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

Back

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

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

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

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have bends.

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

What is the equation of a linear function?

Back

The general form of a linear function is y = mx + b.