We are given the following relationships:

1. $x = 2y$ (x is twice y)
2. $z = x + 3$ (z is three more than x)

Now, substitute $x = 2y$ into the equation for $z$:

$z = (2y) + 3$

Thus, the function for $z$ in terms of $y$ is:

$z(y) = 2y + 3$

Would you like further explanation or examples of similar problems?

Here are 5 related questions to expand on this concept:

1. If $x = 3y$ and $z = 4x - 5$, how would you express $z$ as a function of $y$?
2. What is the inverse function of $z(y) = 2y + 3$?
3. If $z(y) = 2y + 3$, what is $z$ when $y = 5$?
4. Can you graph the function $z(y) = 2y + 3$? What does the slope represent?
5. What happens to $z(y)$ if $y$ becomes negative?

Tip: When translating a word problem into a function, carefully identify all relationships between variables before proceeding with substitutions.