 Hi and welcome to the session. My name is Shashri and I am going to help you with the following question. Question says, examine the following functions for continuity. D part is fx is equal to modulus of x minus 5. Let us now start the solution. We are given fx is equal to modulus of x minus 5. The function can be restated as fx is equal to x minus 5. Greater than equal to 5, fx is equal to minus x minus 5 for less than 5. First of all let us consider fx is equal to x minus 5 for x greater than equal to 5. Now we know this is a polynomial function and polynomial function is continuous at all real values. So even function f is continuous at all positive real numbers greater than equal to 5. So we can write function f is continuous all positive real numbers greater than equal to 5. Let us consider function fx is equal to minus x minus 5 for x less than 5. Now it can be written as fx is equal to minus x plus 5. Now again this is a polynomial function and polynomial function is continuous at all real numbers. So function f is continuous at all real numbers less than 5. Now we get function f is continuous at every real number. We have already proved that these two functions being polynomial functions are continuous. So the function f given by fx is equal to modulus of x minus 5 is also continuous. Function f is continuous function. This is our required answer. This completes the session. Hope you understood the session. Goodbye.