https://file.aiquickdraw.com/mathbot/file/17303038916818iunnry1.jpg

To plot the lattice points of the inverse, let's find the coordinates of the points on the original function \( f(x) = 2^{-x+5} + 4 \), then switch each \( (x, y) \) pair to \( (y, x) \) for the inverse.

The function \( f(x) \) has these visible lattice points:
1. \( (1, 9) \)
2. \( (2, 8) \)
3. \( (3, 6) \)
4. \( (5, 4) \)

For the inverse, swap the \( x \) and \( y \) values in each coordinate:
1. \( (9, 1) \)
2. \( (8, 2) \)
3. \( (6, 3) \)
4. \( (4, 5) \)

These are the lattice points you should plot for the inverse function. Place these points on the graph at:
- \( (9, 1) \)
- \( (8, 2) \)
- \( (6, 3) \)
- \( (4, 5) \)

Would you like further details on the inverse function or additional assistance?

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**Related Questions:**
1. How do you find the inverse of an exponential function?
2. What is the process to determine lattice points on a function graph?
3. Why do we swap \( x \) and \( y \) values when finding the inverse points?
4. What transformations affect the graph of an exponential function like \( f(x) = 2^{-x+5} + 4 \)?
5. How would the inverse function graph differ if there was a horizontal shift in \( f(x) \)?

**Tip:** When plotting an inverse, always check for symmetry along the line \( y = x \).

The function f(x) = 2^{-x+5} + 4 is graphed below. Plot all lattice points of the inverse. Use the labeled points as your guide.

Understand how to find and plot lattice points of the inverse function for f(x) = 2^{-x+5} + 4. This guide covers the process of identifying points on the original function and swapping coordinates to find inverse lattice points. Suitable for high school math students.

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