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?

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 $y = x$.