Comparing Linear and Nonlinear Functions (Week #7)

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 rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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, meaning the ratio of the change in y to the change in x is the same for all intervals.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input (x-value) corresponds to more than one output (y-value).

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 y when x = 0.

Front

If a function is represented by the equation y = 2x + 3, is it linear or nonlinear?

Back

It is a linear function because it can be expressed in the form y = mx + b.

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

How do you determine if a function represented by a graph is linear?

Back

A function represented by a graph is linear if the graph is a straight line.

Front

What is the significance of a constant ratio in a linear function?

Back

A constant ratio indicates that the function has a consistent rate of change, which is a defining characteristic of linear functions.