https://file.aiquickdraw.com/mathbot/file/1725470472038njif3liz.jpg

The problem in the image asks for the equation of a function \( g(x) \) which is derived from the given function \( f(x) = x^2 \). The transformations described are:

1. **Horizontal compression by a factor of 3**: When a function is horizontally compressed by a factor of 3, the transformation involves multiplying the input by 3. The function becomes \( f(3x) \).

2. **Shift to the right by 4 units**: A horizontal shift to the right by 4 units translates the function by subtracting 4 from the input. So the function becomes \( f(3(x - 4)) = (3(x - 4))^2 \).

Thus, the equation of the new function \( g(x) \) after these transformations is:

\[
g(x) = (3(x - 4))^2
\]

Would you like further details or have any other questions?

Here are five related questions for further exploration:
1. What would the equation be if the function was shifted left instead of right?
2. How would the graph change if it was reflected over the x-axis?
3. What happens to the vertex of the parabola after the transformations?
4. How does a vertical stretch differ from a horizontal compression?
5. Can you describe the effect of applying both a vertical and horizontal stretch to the graph?

**Tip:** When dealing with function transformations, always consider the order of operations: perform stretching/compressing first, followed by shifting.

The graph of f(x) = x^2 is given below. Write the equation of a function g(x) which would first compress the graph horizontally by a factor of 3, then shift it 4 units to the right.

This lesson covers how to apply function transformations to the quadratic function f(x) = x^2, including a horizontal compression by a factor of 3 and a shift 4 units to the right. Suitable for students in Grades 9-11.

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