8.F.3 Review - Linear vs. Nonlinear

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 f(x) = 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 create a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, cubic, or exponential.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x and y values. This means that the ratio of the change in y to the change in x will be the same for all pairs of values.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is 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 line crosses the y-axis. It represents the value of y when x is 0.

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

Give an example of a linear function.

Back

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

Front

Give an example of a nonlinear function.

Back

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

Front

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

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph is curved, indicating a variable rate of change.

Front

What does it mean if a function has more than one output for a single input?

Back

If a function has more than one output for a single input, it is not a function according to the definition of a function in mathematics.