Question

the function ( f(x)=-log _{2}(x - 4)+1 ) is graphed below. plot all lattice points of the inverse. use the labeled points as your guide. click on the graph to plot a point. click a point to delete it.

Explanation:

Step1: Find lattice points on \(f(x)\)

First, identify lattice points (integer coordinates) on \(f(x) = -\log_2(x-4) + 1\):

• When \(x=5\): \(f(5) = -\log_2(1) +1 = 0 +1 =1\) → point \((5,1)\)
• When \(x=6\): \(f(6) = -\log_2(2) +1 = -1 +1 =0\) → point \((6,0)\)
• When \(x=8\): \(f(8) = -\log_2(4) +1 = -2 +1 =-1\) → point \((8,-1)\)
• When \(x=4\) is undefined (asymptote), so no point here.

Step2: Swap coordinates for inverse

The inverse function's points are \((y,x)\) of \(f(x)\)'s points:

• Swap \((5,1)\) → \((1,5)\)
• Swap \((6,0)\) → \((0,6)\)
• Swap \((8,-1)\) → \((-1,8)\)

Answer:

Plot the points \((1,5)\), \((0,6)\), and \((-1,8)\) on the graph.