Answer:
To graph the equation y = -log(x-2) + 3, we can start by examining some key points on the graph.
When x = 3, we have y = -log(3-2) + 3 = -log(1) + 3 = 0 + 3 = 3. So, the point (3, 3) lies on the graph.
When x = 2.5, we have y = -log(2.5-2) + 3 = -log(0.5) + 3. Since the logarithm of a number less than 1 is negative, this expression will yield a positive value. So, y is positive.
We can generalize that for any x value less than 2, the expression x-2 will be negative, and taking the logarithm of a negative number is undefined. Therefore, the graph will not extend to the left of x = 2.
For larger values of x, the expression x-2 will be positive, and we can find the corresponding y values.
Let's plot these points and trace a curve that represents the graph.
