The graph you provided shows the function $f(x) = |x|$, which is the standard absolute value function. The problem asks to transform $f(x)$ by shifting it up 4 units and right 5 units, and then draw the resulting graph, $g(x)$, and write its formula.

Steps to find the transformed function $g(x)$:

1. Horizontal Shift (Right by 5 units): To shift a function to the right by 5 units, we replace $x$ with $(x - 5)$. So, the function becomes $|x - 5|$.
2. Vertical Shift (Up by 4 units): To shift the graph up by 4 units, we add 4 to the function. So, the new function becomes $|x - 5| + 4$.

Thus, the transformed function is: $g(x) = |x - 5| + 4$

Graph Description:

• The vertex of the original absolute value function $f(x) = |x|$ is at $(0, 0)$.
• After shifting it right by 5 units and up by 4 units, the vertex of $g(x) = |x - 5| + 4$ will be at $(5, 4)$.
• The graph will still have the same "V" shape, but it will be moved to this new vertex.

Final Answer:

The transformation of $f(x) = |x|$ is: $g(x) = |x - 5| + 4$

Would you like a more detailed explanation or have any questions?

Here are five related questions to explore:

1. How would you shift the graph left by 3 units and down by 2 units?
2. What would happen to the graph if you reflected it over the x-axis?
3. How does shifting affect the domain and range of the function?
4. Can you describe how to vertically stretch or compress the absolute value graph?
5. What is the general formula for a translated absolute value function?

Tip: When transforming graphs, always handle horizontal and vertical shifts separately to avoid confusion.