Problem
The function \( f(x)=3^{-x-1}-2 \) is graphed below. Plot all lattice points of the inverse. Use the labeled points as your guide. Draw Graph Reset Click on the graph to plot a point. Click a point to delete it.
Solution
Step 1 ：1. Write the inverse of the function: \( y = 3^{-x-1} - 2 \) becomes \( x = 3^{-y-1} - 2 \).
Step 2 ：2. Solve for y: \( y = -(\log_{3}(x+2) + 1) \).
Step 3 ：3. Determine the lattice points: Evaluate the inverse function for integer values of x and check if they give integer values for y.
