Determine whether each graph, equation, or table represents...

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.
$$\begin{array}{|c|c|}
\hline x & y \\
\hline-4 & 13 \\
\hline-2 & 0 \\
\hline 0 & 4 \\
\hline 2 & 0 \\
\hline
\end{array}$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Linear Function

A linear function is one where the relationship between the independent and dependent variables is represented by a straight line when graphed. It follows the form y = mx + b, where m is the constant rate of change (slope) and b is the y-intercept, meaning that for every equal increment in x, y increases or decreases by a constant amount.

Constant Rate of Change

The constant rate of change is the defining feature of a linear function. It means that the change in y is uniform with respect to the change in x. This can be determined by checking if the difference between consecutive y-values divided by the difference between their corresponding x-values remains the same throughout the data set.

Nonlinear Function

A nonlinear function does not have a constant rate of change and does not graph as a straight line. In these functions, as x changes, the rate at which y changes also varies, leading to curves or other complex patterns in the graph.

Interpreting Tables to Determine Function Type

One method to determine whether a function is linear or nonlinear is to analyze a table of values. By computing the differences in y for equal increments of x, you can check for a constant rate of change. If the differences are constant, the function is linear; if they differ, the function is nonlinear.

Transcript

Please give Ace some feedback