Continuity of the function f(x)=|x-5|

The function f(x)=|x-5| can be broken down into two cases: when x is less than 5 and when x is greater than or equal to 5.

Case 1: x < />
- For x < 5,="" the="" function="" f(x)="" becomes="" f(x)="-(x-5)," which="" simplifies="" to="" f(x)="5-x." />
- This function is a linear function with a slope of -1, which means it is continuous for all real numbers.

Case 2: x >= 5
- For x >= 5, the function f(x) remains f(x) = x-5.
- This is also a linear function with a slope of 1, making it continuous for all real numbers.

Overall Continuity
- Since both cases of the function f(x)=|x-5| are continuous for all real numbers, the function as a whole is also continuous.
- The function has no breaks or jumps in its graph, and it can be drawn without lifting the pen from the paper.

In conclusion, the function f(x)=|x-5| is continuous for all real numbers.