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The problem asks to translate the graph of the function \( f(x) = |x| - 5 \) 1 unit to the left, and then find the resulting function \( g(x) \).

To translate a function to the left by 1 unit, we replace \( x \) with \( x + 1 \) in the function. So, the translation of \( f(x) \) by 1 unit left will be:

\[
g(x) = |x + 1| - 5
\]

Thus, the translated function is:

\[
g(x) = |x + 1| - 5
\]

Would you like further details or explanations on this?

### Here are 5 related questions to explore:
1. How do you translate a graph to the right instead of the left?
2. What happens when you translate a graph vertically instead of horizontally?
3. How would the graph change if you translated it by 2 units left?
4. How does the translation affect the vertex of an absolute value function?
5. What other transformations can be applied to the graph of an absolute value function?

### Tip:
When translating a graph horizontally, adding a value inside the function moves the graph in the opposite direction. For example, \( x + 1 \) moves the graph to the left, while \( x - 1 \) moves it to the right.

Let f(x) = |x| - 5. Write a function g(x) whose graph is a translation 1 unit left of the graph of f(x).

Learn how to translate the absolute value function f(x) = |x| - 5 by 1 unit to the left. This problem covers the concept of graph transformations and function translation, specifically horizontal shifts, for students in Grades 8-10.

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