Video: Determining Whether a Given Graph Is Linear or Nonlinear

Determine whether the figure represents a linear or a nonlinear function.

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Video Transcript

Determine whether the figure represents a linear or a nonlinear function.

Here are a few things we know about a linear function. In mathematics, a linear function from the real numbers to the real numbers is a function whose graph is a line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.

So first of all, the graph needs to be a line. And for something to be proportional, the input value, which is 𝑥, and the output value, which is 𝑦, will be proportional. 𝑦 will always be four times larger than 𝑥. So looking at our figure, we do not have a straight line. Therefore, the figure that is represented here will be a nonlinear function.

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