Answer:
In conclusion, the formula for g(x), the graph shifted down 5 units and right 2 units compared to f(x), is y = f(x - 2) - 5.
Explanation:
The formula for the graph g(x), which is a shifted version of f(x), can be determined by applying the shift to the original formula for f(x).
To shift the graph down 5 units, we subtract 5 from the original formula. So if the original formula for f(x) is y = f(x), the formula for g(x) would be y = f(x) - 5.
To shift the graph right 2 units, we replace x in the formula with (x - 2). So the formula for g(x) becomes y = f(x - 2) - 5.
Now, let's address the use of sqrt(x) as sqrt(x) in the answer.
The expression sqrt(x) represents the square root of x. The square root of a number is the value that, when multiplied by itself, gives the original number. For example, sqrt(9) is 3 because 3 multiplied by itself equals 9.
Using sqrt(x) as sqrt(x) instead of the traditional radical symbol (√x) helps to avoid any confusion or formatting issues when writing mathematical expressions online or in text. Both sqrt(x) and √x represent the same concept of the square root of x.