https://file.aiquickdraw.com/mathbot/file/1726812726119zi4txcrj.jpg

Select the correct answer below:

f(x)=−3|x−3|−3

f(x)=3|x−3|−3

f(x)=−3|x+3|−3

f(x)=3|x+3|−3

f(x)=−3|x−3|+3

The graph shows a V-shaped curve, which suggests it is an absolute value function of the form \( f(x) = a|x - h| + k \), where \( (h, k) \) is the vertex of the function, and \( a \) affects the slope and direction of the lines (whether the V opens upwards or downwards).

### Key observations:
- The vertex is at \( (3, -3) \).
- The graph opens downwards, meaning \( a \) must be negative.
- The function is shifted 3 units to the right (so the expression should be \( |x - 3| \)).

### Analyzing the given options:
1. \( f(x) = -3|x - 3| - 3 \) seems like a good fit, as it reflects the downward opening, the vertex at \( (3, -3) \), and the correct transformation.
2. The other options either have incorrect signs for \( a \) (like the positive ones that would open upwards), or incorrect horizontal shifts (like those involving \( x + 3 \)).

Thus, the correct answer is:

\[ f(x) = -3|x - 3| - 3 \]

Would you like further details or clarifications? 

### Related Questions:
1. How do you find the vertex of an absolute value function?
2. How does the coefficient \( a \) in \( f(x) = a|x - h| + k \) affect the graph?
3. What is the effect of the transformation \( |x - h| \) on the graph of the absolute value function?
4. How can you determine whether the graph opens upwards or downwards?
5. How do shifts in \( x \) and \( y \) change the position of the graph?

### Tip:
When solving absolute value problems, always identify the vertex and check the direction (upwards or downwards) to quickly narrow down the correct function.

Which of the following functions is shown in the graph below? Select the correct answer below: f(x)=−3|x−3|−3, f(x)=3|x−3|−3, f(x)=−3|x+3|−3, f(x)=3|x+3|−3, f(x)=−3|x−3|+3

Analyze the absolute value function f(x) = -3|x - 3| - 3 and its graph, which shows a V-shape with the vertex at (3, -3) and the function opening downward. This problem covers algebraic concepts related to absolute value transformations, suitable for Grades 10-12.

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