The graph provided shows the function $g(x)$, which is a transformation of the function $f(x) = |x|$.

The graph appears to have the following transformations:

1. Reflection: The graph reflects the absolute value function over the x-axis to the left of $x = 0$ (i.e., for $x < 0$).
2. Vertical Translation: The vertex of the graph is moved downward to $(0, -3)$.
3. Shift: The absolute value function seems to be unchanged in terms of stretch or compression, but shifted downward by 3 units.

Thus, the transformation can be described as a vertical shift downward by 3 units and possibly a reflection of the left side of the function.

The function $g(x)$ can be written as: $g(x) = -|x| - 3$ This means the graph has undergone:

• A vertical reflection (for negative values of $x$).
• A downward shift of 3 units.

Would you like further explanation on how to derive the transformation, or do you have any specific questions?

Here are 5 related questions:

1. How do you determine reflections in function transformations?
2. What effect does a vertical shift have on a graph?
3. How would the function change if the graph were shifted 2 units to the right instead?
4. What does it mean when a function is reflected over the x-axis?
5. Can you apply multiple transformations, such as both horizontal and vertical shifts?

Tip: When shifting a function vertically, the transformation is directly applied to the output of the function, which is why you see constants added or subtracted outside the absolute value term.