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brhum
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How do you graph f(x) = x - [[x]]
brhum said:How do you graph f(x) = x - [[x]]
The function f(x) = x - [[x]] is a piecewise function, where [[x]] represents the greatest integer less than or equal to x. This means that the graph of the function will have a sawtooth shape, with the slope changing at every integer value of x.
To graph this function, plot points using the equation for different values of x. For example, when x = 0.5, f(x) = 0.5 - [[0.5]] = 0.5 - 0 = 0.5. Plot this point on the graph. Repeat for different values of x, and then connect the points to create the sawtooth shape.
The graph of this function looks like a series of diagonal lines, with the slope changing at every integer value of x. It has a repeating sawtooth pattern.
The domain of this function is all real numbers, as there are no restrictions on the values of x. The range of the function is also all real numbers, as the function can output any real number depending on the input value of x.
This function can be used to model situations where there is a repeating pattern or cycle, such as in the stock market or population growth. It can also be used to calculate the distance between two points on a graph with a sawtooth pattern.