Question

f(x)= (x/3)+2+(3/x)
determine the values of x for which the graph is continuous?

Answer 1

Refer to the attachment.

Answer 2

To me it, looks like very value but zero...(3/0) D.N.E

Answer 3

Visually, notice the asymptote is at x = 0 (such that the x values approach 0 infinitely closely from the negative and positive side).

Also, algebraically, notice that x can be anything in x/3 and 2 is always and x can be anything EXCEPT ZERO in 3/x therefore for the summation of all these: x/3 + 2 + 3/x, one must consider all the invidual constraints that each term brings but it is only the 3/x term which brings a constraint of x ≠ 0 therefore, x/3 + 2 + 3/x holds for all values of x except 0 so the function is continuous everywhere except 0.