Function M8 Lesson 15 Review

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change, meaning the ratio of the change in the y value to the change in the x value is constant.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph as a straight line. The rate of change is not constant, meaning the ratio of the change in the y value to the change in the x value varies.

Front

How can you determine if a table represents a linear function?

Back

A table represents a linear function if the ratio of the change in the y values to the change in the x values is constant for all pairs of points.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If an input has more than one output, it is not a function.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x). It represents the steepness of the line.

Front

What is the y-intercept of a linear function?

Back

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

Front

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

Back

A linear equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept. A nonlinear equation cannot be expressed in this form and may include variables raised to a power other than one.

Front

How can you identify a linear graph?

Back

A linear graph is identified by its straight line. If the graph curves or has bends, it is nonlinear.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which represents a straight line with a slope of 2 and a y-intercept of 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which represents a parabola and does not form a straight line.