What is the difference between a linear function and a nonlinear function? Explain what each looks like when represented as a table and as a graph.
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A linear function is a function where the graph of the function is a straight line. It can be represented in the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept. When represented as a table, the values of x and y will have a constant rate of change. When represented as a graph, the line will be a straight line that extends infinitely in both directions.
On the other hand, a nonlinear function is a function that does not form a straight line when graphed. This type of function does not have a constant rate of change and can take on various shapes, such as curves, parabolas, or exponential growth or decay. When represented as a table, the values of x and y will not have a constant rate of change. When represented as a graph, the function will not form a straight line and may have multiple peaks or valleys.
In summary, the main difference between a linear function and a nonlinear function is the shape of their graphs. Linear functions form straight lines, while nonlinear functions do not.