f(x) = 1/x
To understand the function f(x) = 1/x, let’s break it down:
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To understand the function f(x) = 1/x, let’s break it down:
1. Definition of a Function:
In mathematics, a function is a rule that assigns each element from one set, called the domain, to a unique element of another set, called the range. In simpler terms, a function takes an input and produces an output. In this case, f(x) represents the function, where x is the input, and the output is calculated using the formula 1/x.
2. Domain and Range:
The domain of a function is the set of all possible values for the input variable, while the range is the set of all possible values for the output variable. For the function f(x) = 1/x, the domain consists of all real numbers except 0 because division by zero is undefined. The range includes all real numbers excluding zero, as any non-zero input will produce a non-zero output.
3. Graph of the Function:
Plotting the graph of the function f(x) = 1/x helps us visualize its behavior. The graph starts at positive infinity on the right and negative infinity on the left of the y-axis. The function approaches zero as x approaches positive or negative infinity. It also has a vertical asymptote at x = 0, meaning that the graph approaches infinity from both sides as x gets closer to zero.
4. Symmetry:
The function f(x) = 1/x exhibits symmetry across the y-axis. This means that for any value of x, the corresponding y-value will be the same as if we replaced x with its negative counterpart. In other words, f(x) = f(-x).
5. Behavior as x approaches positive or negative infinity:
As x gets larger and larger (approaching positive infinity), the function f(x) = 1/x approaches 0. Similarly, as x gets smaller and smaller (approaching negative infinity), f(x) also approaches 0. This is because the function represents the reciprocal of x, where the larger the value of x, the closer its reciprocal (1/x) gets to zero.
I hope this explanation helps you understand the function f(x) = 1/x and its various properties. If you have any further questions, feel free to ask!
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