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Create an exponential graph with the formula using the 1st and 2nd differences of squares in the first photo.

It seems there was an issue with calculating the values of \(3^x\) for negative integers. I will modify the function to ensure correct handling of negative exponents.

Let me fix that and generate the exponential graph again.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any further questions, feel free to ask! Here are five questions related to the topic that you may want to explore:

1. How can we find the first and second differences for the quadratic function \( y = 3x^2 \)?
2. What are the steps to identify whether a function is linear, quadratic, or exponential using differences?
3. How does the behavior of the graph of \( y = 3^x \) change as \( x \) increases or decreases?
4. How do you graph multiple functions on the same grid and compare them visually?
5. What real-life phenomena can be modeled by exponential functions like \( y = 3^x \)?

**Tip:** When working with exponential functions, small changes in \( x \) can lead to rapid changes in \( y \), making the graph increase sharply as \( x \) grows.

Explore the exponential function y = 3^x by calculating the first and second differences, classifying it as exponential, and graphing it. Suitable for Grades 9-12, this problem demonstrates how to analyze and compare different types of functions.

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