https://file.aiquickdraw.com/mathbot/file/1726925442485qiurwcm3.jpg

The graph in the image represents \( y = f(x) - 3 \), and the question asks for the value of \( x \), rounded to the nearest whole number, when \( f(x) = 4 \).

To solve this:

1. Rearrange the equation to solve for \( f(x) \):
   \[
   f(x) - 3 = 4
   \]
   \[
   f(x) = 4 + 3 = 7
   \]
   So, we need to find the value of \( x \) for which \( f(x) = 7 \).

2. Now, observe the graph. The curve \( y = f(x) - 3 \) is plotted. When \( f(x) = 7 \), the value of \( y \) on the graph will be:
   \[
   y = f(x) - 3 = 7 - 3 = 4
   \]
   Therefore, we need to find the \( x \)-coordinate when \( y = 4 \) on the graph.

3. From the graph, at \( y = 4 \), the corresponding value of \( x \) is approximately **6**.

Thus, the value of \( x \) where \( f(x) = 4 \) is **6** (rounded to the nearest whole number).

Do you want more details or have any other questions?

Here are 5 related questions:
1. How do you determine the vertical shift in a function from its graph?
2. What does the function \( f(x) - 3 \) represent in terms of transformations?
3. How do you interpret the horizontal stretch/compression in graphs?
4. What is the general approach to solving equations involving functions graphically?
5. How do you estimate values between grid lines on a graph?

**Tip:** For transformed functions, always first reverse the transformations to identify the original function behavior.

For which value of x, rounded to the nearest whole number, must f(x) = 4 given the graph of y = f(x) - 3?

Learn how to determine the value of x for which f(x) = 4 based on the graph of y = f(x) - 3. This problem explores graph interpretation and function transformations, suitable for students in Grades 8-10.

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