f(x) = log(x-2) +2
To plot the graph let us draw the graph of log(x-2) and then we shift the entire graph by 2 upsides.
What is the shifting of the graph?
Assume that a > 0 and f is a function. Use the formulas g(x) = f(x) + a and h(x) = f(x) to define functions g and h.
Then,
By moving the graph of f up a unit, the graph of g is produced.
By moving the graph of f down a unit, the graph of h is produced.
The domain of f is shared by g and h.
Every number in the range of f is multiplied by a to get the range of g, and every number in the range of f is multiplied by a to get the range of h.
The solution to the problem.
f(x) = log(x-2)+2
let us make the graph of f(x)= log(x-2), so at x = 3 f(x) = 0, and at x=2 f(x) is tending to -∞. The graph is not valid for x<2, as log's domain does not include it. Hence the graph is
After shifting the graph by 2 we get
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