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To solve this correctly:

You are given that the graph of \( g(x) \) is the graph of the parent function \( f(x) = x \) translated 5 units left and 1 unit up.

1. **Horizontal Translation:**
   - Translation to the left by 5 units means we will adjust the \( x \)-term in the form \( g(x) = f(x - h) \) where \( h \) is negative for a left shift. So, we write:
     \[
     g(x) = (x + 5)
     \]

2. **Vertical Translation:**
   - A translation 1 unit up affects the constant term by adding 1 to the equation. So, we add 1.

Thus, the equation becomes:
\[
g(x) = (x + 5) + 1
\]

### Answer from the dropdown:
- First dropdown: \(-5\) (because moving left by 5 units corresponds to \( x + 5 \)).
- Second dropdown: \(1\) (since we move the function up by 1 unit).

Do you need further clarifications or details? Here are five related questions:

1. How do vertical and horizontal shifts affect the graph of a linear function?
2. How would the equation change if the function was translated right instead of left?
3. What is the general form of a function after both horizontal and vertical translations?
4. Can you explain how translations affect the slope of the line?
5. How would the graph change if instead of a shift, the function was reflected?

**Tip:** Always remember that horizontal shifts inside the parentheses have the opposite sign: shifting left uses "+", and shifting right uses "-".

The graph of g(x) is the graph of the parent function f(x) = x translated 5 units left and 1 unit up. The equation of the function g(x) is: g(x) = (x - ___) + ___.

Learn how to solve problems involving the translation of linear functions. This example shows how to translate the parent function f(x) = x by 5 units to the left and 1 unit up to find the equation of the new function g(x). Suitable for students in Grades 9-10.

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