Question: Write an equation for a function that has the graph with the shape of $y=\lvert x \rvert$, but shifted left 9 units and up 2 units. $f(x)= $
1. **State the problem:** We need to find the equation of a function that looks like $y=\lvert x \rvert$ but is shifted left by 9 units and up by 2 units.
2. **Recall the base function:** The base function is $y=\lvert x \rvert$.
3. **Understand shifts:**
- Shifting left by 9 units means replacing $x$ with $x+9$ inside the absolute value.
- Shifting up by 2 units means adding 2 to the whole function.
4. **Write the new function:**
$$f(x) = \lvert x + 9 \rvert + 2$$
5. **Explanation:**
- The $x+9$ inside the absolute value shifts the graph left by 9.
- The $+2$ outside shifts the graph up by 2.
6. **Final answer:**
$$\boxed{f(x) = \lvert x + 9 \rvert + 2}$$