The function provided is $g(x) = x + 4$.

Step 1: Identify the Parent Function

The function $g(x) = x + 4$ is a linear function, and the parent function for this is simply $f(x) = x$.

Step 2: Identify the Transformation

Comparing $g(x) = x + 4$ to the parent function $f(x) = x$, the addition of 4 means that the graph is shifted up by 4 units.

Conclusion:

• The parent function is linear.
• The transformation is a translation up 4 units.

Thus, the correct option is:

• Linear; translation up 4 units.

Would you like a detailed explanation on transformations or have any further questions?

Related Questions:

1. What is a vertical translation in function transformations?
2. How does adding a constant affect the graph of a linear function?
3. What are the key characteristics of a linear function?
4. How do you identify horizontal transformations in functions?
5. What happens when you subtract a constant from a linear function?

Tip: When identifying transformations, focus on how constants added or subtracted from $x$ or the entire function affect the graph.