linear vs. Nonlinear relationships Practice

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, such as parabolas or circles.

Front

How can you identify a linear function from its equation?

Back

If the equation can be written in the form y = mx + b, where m and b are constants, it is a linear function.

Front

What is the slope of a linear function?

Back

The slope of a linear function (m) 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 an example of a linear function?

Back

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

Front

What is an example of a nonlinear function?

Back

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

Front

How can you tell if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of a.