Question Video: Determining Whether a Given Figure Represents a Linear or Nonlinear Function Mathematics

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

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Video Transcript

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

We begin by recalling that a linear function is represented graphically as a straight line. The function is written in the form 𝑓 of 𝑥 is equal to 𝑚𝑥 plus 𝑏, where 𝑚 is the slope of the line and 𝑏 is the 𝑦-intercept. If 𝑚 is greater than zero, we have a positive slope and our function slopes upwards from left to right. In a similar way, if 𝑚 is less than zero, the slope of our graph is negative and the graph slopes downwards from left to right. Finally, if 𝑚 is equal to zero, we have a constant function, and this is represented graphically as a horizontal line.

It is clear that the graph in the figure is not a straight line, and we can therefore conclude that it represents a nonlinear function.

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