9 Weeks Test

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function that does not form a straight line when graphed. It has a variable rate of change and can include curves, parabolas, and other shapes.

Front

What is an increasing interval in a function?

Back

An increasing interval is a section of the graph where the function's values rise as the input values increase.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a section of the graph where the function's values fall as the input values increase.

Front

What is a constant interval in a function?

Back

A constant interval is a section of the graph where the function's values remain the same as the input values change.

Front

How can you determine if a function is increasing, decreasing, or constant?

Back

You can determine this by analyzing the slope of the function over different intervals. If the slope is positive, the function is increasing; if negative, it is decreasing; and if zero, it is constant.

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 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, represented by the value of b in the equation y = mx + b.

Front

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

Back

A linear equation represents a straight line and has a constant rate of change, while a nonlinear equation represents a curve and has a variable rate of change.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which has a constant slope of 2.