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

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SUMMARY

The discussion focuses on solving the unit step function f(t) = 6u(-t) + 6u(t+1) - 3u(t+2) for t = -1. The user initially misinterprets the unit step function, leading to an incorrect calculation of 3 instead of the correct answer, 9. The key takeaway is that u(x) equals 1 at x=0, which is crucial for evaluating the function correctly. Understanding the behavior of the unit step function is essential for accurate problem-solving in this context.

PREREQUISITES
  • Understanding of the unit step function, u(t)
  • Basic knowledge of piecewise functions
  • Familiarity with evaluating mathematical expressions
  • Concept of function continuity at specific points
NEXT STEPS
  • Study the properties of the unit step function, u(t), in detail
  • Learn about piecewise function evaluation techniques
  • Explore applications of the unit step function in control systems
  • Practice solving similar problems involving unit step functions and piecewise definitions
USEFUL FOR

Students studying calculus, particularly those focusing on piecewise functions and the unit step function, as well as educators seeking to clarify these concepts in a teaching context.

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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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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.
 

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