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 "-".