Identifying 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 a curve or any other shape that is not a straight line.

Front

How can you identify a linear function from its equation?

Back

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

Front

What is the slope of a linear function?

Back

The slope of a linear function (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 represent in a linear function?

Back

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

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.

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 difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

Front

How can you tell if a function is linear by looking at a table of values?

Back

If the differences between consecutive y-values are constant for equal intervals of x, the function is linear.