if x is twice y, and z is three more than x, write z as a function of y

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.

If x is twice y, and z is three more than x, write z as a function of y.

Learn how to express z as a function of y when x is twice y and z is three more than x. This problem explores key algebraic concepts such as linear functions and solving equations. Suitable for students in Grades 6-8.

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