Fill in the table for f(x) and g(x). Then, graph each function below:
X f(x) = log2 x g(x) = -log2(x - 2) + 1
-1
0
1
2
3
4
5
6
To fill in the table, we need to plug in the values of x into the functions:
For f(x) = log2(x):
X f(x) = log2 x
-1 not defined
0 not defined
1 0
2 1
3 1.585
4 2
5 2.322
6 2.585
For g(x) = -log2(x - 2) + 1:
X g(x) = -log2(x - 2) + 1
-1 not defined
0 not defined
1 not defined
2 1
3 0
4 0.585
5 1
6 1.322
To graph the functions, we can plot the points we found above, but the domain must be restricted to the values where the function is defined (x > 0).
The graph of f(x) = log2(x) will start from (1,0) and rise steadily as x increases.
The graph of g(x) = -log2(x - 2) + 1 will start from (2,1) and decrease towards 1 as x increases.
Please note that the values at x = -1, 0, and 1 are not included in the graph as they are not defined.