5. In our proof that constant functions are continuous, we used the fact that given any e > 0, a choice of any 8 > 0 will work in the formal definition of limit. Use a graph to explain why this makes intuitive sense. (This exercise de- pends on Section 1.3.) 6. In our proof that linear functions are continuous, we used the fact that given any e > 0, the choice of 8 = will Iml work in the formal definition of limit. Use a graph to ex- plain why this makes intuitive sense. (This exercise depends on Section 1.3.) 7. Given the following function f, define f (1) so that f is con- tinuous at x = 1, if possible: f ( x ) =: x2 - 2x+1 x2 - 6x +5' 8. Given the following function f, define f (1) so that f is con- tinuous at x = 1, if possible: 3x - 1, ifx 1. Each function in Exercises 9-12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f. 9. lim f(x) = 2, lim f(x) = 2, f(-1) = 1. x - -1- x- -1+