https://file.aiquickdraw.com/mathbot/file/1726619955318qimvqvpe.jpg

We are asked to identify which function has the same **y-intercept** as the function whose graph is shown.

### Steps to solve:
1. **Locate the y-intercept**: The y-intercept is the point where the graph crosses the y-axis (when \(x = 0\)). From the graph, it looks like the y-intercept is at \(y = -2\).
   
2. **Find the y-intercept for each function**:
   - \(f(x) = 2^x\): When \(x = 0\), \(f(0) = 2^0 = 1\). The y-intercept is \(1\).
   - \(f(x) = 2x^5 + 5x^3 - 4x^2 + 10\): When \(x = 0\), \(f(0) = 10\). The y-intercept is \(10\).
   - \(f(x) = -10x^5 + 3x\): When \(x = 0\), \(f(0) = 0\). The y-intercept is \(0\).
   - \(f(x) = x^4 - 2\): When \(x = 0\), \(f(0) = 0^4 - 2 = -2\). The y-intercept is \(-2\).

### Conclusion:
The function that has the same y-intercept (\(-2\)) as the graph shown is **\(f(x) = x^4 - 2\)**.

Would you like more details or have any questions about the process?

Here are five related questions:
1. How can you quickly find the y-intercept of any function?
2. What is the significance of the y-intercept in real-world applications?
3. How do different powers of \(x\) affect the shape of a graph?
4. Why does the exponential function \(2^x\) have a positive y-intercept?
5. How do you distinguish between different polynomial graphs?

**Tip**: Always substitute \(x = 0\) into a function to find the y-intercept!

Which function has the same y-intercept as the function whose graph is shown?

Learn how to determine which function shares the same y-intercept as the graph shown. Explore the concept of y-intercepts by substituting x = 0 into multiple functions. Suitable for students in Grades 9-11.

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