Piecewise definition for a function

In summary, the function f(t) given is a piecewise function with three parts, (t-1)u(t), -(t-2)u(t-2), and -u(t-4). The middle part of the function is causing difficulty in writing a piecewise definition. Assistance is requested on how to proceed. A list of f(0), f(1), f(2), f(3), f(4), and f(5) is needed. The unit step function, u(t), is defined as 1 for t >= 0 and 0 for t < 0. The function f(t) can be evaluated with these values.
  • #1
jojo1
1
0
Hi i have been given this function

f(t)= (t-1)u(t)-(t-2)u(t-2)-u(t-4)

and have to write a piecewise definition for it.

the middle part of the function is given me problems.

can anyone assist on what to do

Thanks

Jo
 
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  • #2
Calculate f(0),f(1),f(2),f(3),f(4),f(5) (i think this should be enough)
Can u see what to do now?

-- AI
 
  • #3
Does u(t) simply mean 1 for t => 0 and 0 for t < 0
 
  • #4
well i assumed that to be the case,
u(t) is normally the unit step function
(ofcourse i might be doing too much of digital signal processing lately)

-- AI
 

FAQ: Piecewise definition for a function

What is a piecewise definition for a function?

A piecewise definition for a function is a way of defining a function that consists of different rules or formulas for different parts of its domain. This allows for a more specific and precise description of the behavior of the function.

Why would someone use a piecewise definition for a function?

A piecewise definition for a function is often used when the behavior of the function changes at specific points or intervals. It allows for a more accurate representation of the function and can make it easier to analyze and understand the function's behavior.

How do you write a piecewise definition for a function?

To write a piecewise definition for a function, you need to define different rules or formulas for different parts of the function's domain. These rules or formulas should reflect the behavior of the function in each specific part of its domain.

What are the benefits of using a piecewise definition for a function?

Using a piecewise definition for a function can provide a more accurate and detailed description of the function's behavior. It can also make it easier to analyze and graph the function, as well as understand its behavior at different points or intervals.

Are there any limitations to using a piecewise definition for a function?

One limitation of using a piecewise definition for a function is that it can become more complex and difficult to work with if there are a large number of rules or formulas involved. It may also be more challenging to find the overall behavior of the function with a piecewise definition compared to a single, simpler formula.

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