Write a formula for

*V*(*t*)

in terms of

*H*(*t*).

(Note that starting at

*t* = 4

corresponds to a translation.)

To write a formula for \( V(t) \) in terms of \( H(t) \), considering that starting at \( t = 4 \) corresponds to a translation, we can represent this as a time shift in the function.

### Translation and Time Shift

If starting at \( t = 4 \) corresponds to a translation, it implies that the function \( H(t) \) is shifted by 4 units to the right on the time axis. In general, if a function \( H(t) \) is shifted to the right by 4 units, the new function \( V(t) \) can be expressed as:

\[
V(t) = H(t - 4)
\]

This formula indicates that the value of \( V(t) \) at any time \( t \) is the same as the value of \( H(t) \) at a time 4 units earlier.

Would you like more details on function translation or have any specific questions about this? 

Here are 5 related questions you might find interesting:
1. How do you express a vertical translation of a function?
2. What happens to a function if it is translated to the left instead of the right?
3. How would you translate a function both horizontally and vertically?
4. Can you explain how translations affect the graph of a function?
5. What is the difference between horizontal and vertical translations?

**Tip:** Always keep track of the direction of translation when shifting functions horizontally; right shifts involve subtracting from the input, and left shifts involve adding to the input.

Discover how to write a formula for V(t) in terms of H(t), considering a time shift starting at t = 4. Learn about function translation and time shifts in mathematics.

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