How Do You Graph the Function f(x) = x - [[x]]?

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In summary, the function f(x) = x - [[x]] is a piecewise function with a sawtooth shape, where [[x]] represents the greatest integer less than or equal to x. To graph this function, points can be plotted using the equation for different values of x, resulting in a series of diagonal lines with a repeating sawtooth pattern. The domain and range of the function are both all real numbers, making it useful for modeling repeating patterns or calculating distances on a sawtooth graph.
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brhum
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How do you graph f(x) = x - [[x]]
 
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Well that will depend upon what "[[x]]" means! If it is the "floor" function, you should be able to calculate a few values at, say 0.5, 0.7, 0.9, 1.2, 1.4, 1.7, 2.5. 2.7, 2.9 and see for your self.
 
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brhum said:
How do you graph f(x) = x - [[x]]

Do you see that [[x]] is same as [x]? Plotting f(x) should be trivial once you notice that.

(assuming [x] denotes the floor function)
 

1. What is the meaning of "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.

2. How do you graph f(x) = x - [[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.

3. What does the graph of f(x) = x - [[x]] look like?

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.

4. What is the domain and range of f(x) = x - [[x]]?

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.

5. How is the function f(x) = x - [[x]] useful in real-world situations?

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.

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