8.F.3 Review - Linear vs. Nonlinear

Front

What is the definition of 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 the definition of 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

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x is 0.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight-line graph, which has a constant slope.

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 difference between linear and nonlinear equations?

Back

Linear equations represent relationships with a constant rate of change, while nonlinear equations represent relationships with varying rates of change.

Front

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

Back

If the equation can be rearranged into the form y = mx + b, it is linear; otherwise, it is nonlinear.

Front

What is the significance of the degree of a polynomial in determining linearity?

Back

The degree of a polynomial indicates its highest exponent; a polynomial of degree 1 is linear, while degrees greater than 1 indicate nonlinear functions.