piece wise function
A piecewise function, also known as a piecewise-defined function or a hybrid function, is a mathematical function that is defined by multiple sub-functions, each of which applies to a specific interval or set of input values
A piecewise function, also known as a piecewise-defined function or a hybrid function, is a mathematical function that is defined by multiple sub-functions, each of which applies to a specific interval or set of input values.
To understand how a piecewise function works, let’s consider an example:
f(x) =
{
2x + 1 if x < 0
x^2 if x ≥ 0
}
In this example, we have two different sub-functions defined for different intervals. When x is less than 0, the function is defined as 2x + 1. For x greater than or equal to 0, the function is defined as x^2.
For example, if we want to find the value of f(-3), we use the first sub-function since -3 is less than 0. So, we substitute -3 into the first sub-function:
f(-3) = 2(-3) + 1
= -6 + 1
= -5
On the other hand, if we want to find the value of f(2), we use the second sub-function since 2 is greater than or equal to 0:
f(2) = 2^2
= 4
So, the value of the piecewise function f(x) at x = -3 is -5 and at x = 2 is 4.
Piecewise functions can have any number of sub-functions, each defined for a different interval. The intervals can be open (excludes the endpoint) or closed (includes the endpoint). The different sub-functions can be any mathematical expression or formula depending on the specific requirements of the problem or function being defined.
It is important to carefully analyze the given intervals and expressions when working with piecewise functions to ensure correct evaluation and understanding of the function's behavior for different inputs.
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