Final answer:
To determine if the function f(x,y) is continuous everywhere, we need to check if the function is continuous at x=3. To be continuous at x=3, the value of the function from the left side, which is c+y, must be equal to the value of the function from the right side, which is 3-y. Therefore, c = (3-2y) makes the function continuous at x=3.
Step-by-step explanation:
To determine if the function f(x,y) is continuous everywhere, we need to check if the function is continuous at x=3, since that is the only point where the function is defined differently for x≤3 and x>3.
To be continuous at x=3, the value of the function from the left side, which is c+y, must be equal to the value of the function from the right side, which is 3-y. Therefore, we can set c+y = 3-y and solve for c.
Adding y to both sides and rearranging the equation, we get c = (3-2y). So, there is a value for c that makes the function continuous at x=3, and the value of c is (3-2y).