Unit Step Function Homework: Solve f(t) for t = -1

In summary, the conversation is about the difficulty in understanding the unit step function and how it affects the evaluation of a given expression. The person initially thought that u(t) returns 0 for a negative or zero value, but it actually returns 1 at x=0. This misunderstanding led to an incorrect answer of 3, when the correct answer should be 9. The person is seeking clarification on how to handle the unit step function in this situation.
  • #1
jesuslovesu
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Homework Statement


I'm having a bit of difficulty understanding the unit step function
For example
f(t) = 6u(-t) + 6u(t+1) - 3u(t+2)
t = -1


Homework Equations





The Attempt at a Solution



If t = -1 then the way I would do the problem is say that if u(t) returns a negative number or zero then it's zero
6(1) + 6u(0) - 3(1) = 3
However, the answer is 9 so I must be misinterpreting how the unit step function works. Can anyone explain to me how one would handle the unit step function in this situation?
 
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  • #2
The unit step function, u(x) is 1 at x=0, not 0. This is your problem. Try evaluating you expression, taking this into account, and you should get 9 as your answer.
 

1. What is a unit step function?

A unit step function, denoted as u(t), is a mathematical function that has a value of 0 for all negative inputs and a value of 1 for all positive inputs. It is often used to represent a sudden change or "jump" in a system.

2. How do I solve f(t) for t = -1?

To solve f(t) for t = -1, you need to substitute t = -1 into the given function and simplify. For example, if f(t) = 2t + 5, then f(-1) = 2(-1) + 5 = 3.

3. What is the significance of t = -1 in a unit step function?

When t = -1, the unit step function has a value of 0. This means that at t = -1, there is no sudden change or "jump" in the system represented by the function.

4. How is a unit step function related to the Heaviside step function?

The Heaviside step function is a more general form of the unit step function, where it can have a different value for negative inputs. The unit step function is a special case of the Heaviside step function where the value for negative inputs is always 0.

5. Can a unit step function have a value other than 0 or 1?

No, by definition, a unit step function can only have a value of 0 or 1 for all inputs. This is what makes it a step function, as it "jumps" from one value to another at a specific input.

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