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The original function given is \( f(x) = |x| \).

Now, we are asked to shift this function:
1. **Left by 6 units**: Shifting a function left by 6 units modifies the argument of the function. For a shift left, we add 6 to \(x\). So the new function becomes \( |x + 6| \).
2. **Down by 7 units**: Shifting a function down by 7 units means subtracting 7 from the function value. So we subtract 7 from the expression.

Thus, the new equation for the function \(g(x)\) after shifting becomes:
\[
g(x) = |x + 6| - 7
\]

Would you like a detailed breakdown of how shifts in functions work?

Here are 5 related questions:
1. How do horizontal and vertical shifts affect the graph of a function?
2. What happens to the graph of \( f(x) = |x| \) if it is shifted right instead of left?
3. How can you determine shifts based on the equation of a function alone?
4. What would the graph look like if you shifted the function up instead of down?
5. How do reflections (flipping) relate to translations in functions?

**Tip**: Horizontal shifts affect the \(x\)-variable inside the function (e.g., \( x + c \) for left), while vertical shifts affect the entire function by adding or subtracting a constant.

Write an equation of the function g(x) that is the graph of f(x) = |x|, but shifted left 6 units and shifted down 7 units.

Learn how to shift the absolute value function f(x) = |x| left by 6 units and down by 7 units to get the new function g(x) = |x + 6| - 7. This problem demonstrates the concept of function transformations, including horizontal and vertical shifts, suitable for students in Grades 8-10.

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