Are the following statements true or false? Choose True if the statement is always true, and otherwise choose False.

1. If lim j(x) is a real number, and j(-3) is a different real number, we would say that j has a jump discontinuity at x = -3. 2. If f and g are two functions that are continuous on all of R, then the two composite functions fog and go f are also continuous on all 4 R. ? 3. If lim k(x ) does not exist, we would say that k(x ) has a vertical asymptote at x = 8. ? 4. As long as the function f is continuous at x = c, we can plug in x = c to find the limit lim f (a). r-C 3 ? 5. The function f (x) = is continuous at every point in R. 1 +x2 ? 6. A function can have infinitely many jump discontinuities.7. A function can have all of the following, if they occur at different x-values: a removeable discontinuity two vertical asymptotes, and seventeen jump discontinuities. ? 8. If a function g(x ) is continuous at x = 7, then we must have 7 E D. ? 9. A function f (x) can have both a vertical asymptote and a removeable discontinuity at x = 2. ? 10. If a function h (x) has a jump discontinuity at x = 4, we can phrase this more formally by saying the following: the limits lim h(x) and lim h(x) are both real numbers, but they are not the same real number. x-+4+