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The graph you provided appears to represent a square root function. The point \((4, 14)\) is marked on the curve, which suggests that this is an important point for determining the function.

A general form of a square root function is:

\[
y = a \sqrt{x - h} + k
\]

where:
- \(a\) is the vertical stretch or compression,
- \(h\) is the horizontal shift, and
- \(k\) is the vertical shift.

### Observations:
- The graph passes through the point \((4, 14)\).
- The vertex (starting point of the curve) appears to be at \((0, 0)\), which suggests \(h = 0\) and \(k = 0\).

Thus, the function is likely of the form:

\[
y = a \sqrt{x}
\]

Now, using the point \((4, 14)\) to find \(a\):

Substitute \(x = 4\) and \(y = 14\) into the equation:

\[
14 = a \sqrt{4}
\]

Simplifying:

\[
14 = 2a
\]

Solve for \(a\):

\[
a = \frac{14}{2} = 7
\]

Thus, the equation of the square root function is:

\[
y = 7 \sqrt{x}
\]

This represents the curve shown in the graph.

---

Do you want further clarification or details on this? Here are 5 related questions to deepen your understanding:

1. How does changing the value of \(a\) affect the shape of the square root function?
2. What would happen if there was a horizontal or vertical shift in the function?
3. Can you describe how to determine the domain and range of a square root function?
4. How would you find the inverse of the function \(y = 7 \sqrt{x}\)?
5. What role does the vertex \((0, 0)\) play in this type of square root function?

**Tip**: In square root functions, the domain is restricted by the values inside the square root. Make sure \(x - h \geq 0\) to avoid complex numbers!

Write the square root function based on the given graph, which passes through the point (4, 14) and starts from the origin (0, 0).

Learn how to derive the square root function y = 7√x using the given graph passing through (4, 14). This problem involves understanding the transformation of square root functions and applying algebraic concepts to determine the equation. Suitable for Grades 9-10.

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