Question

3. $f(x) = \begin{cases} 3x - 1, & x < 2 \\ x + 3, & x \ge 2 \end{cases}; c = 2$ a) discontinuous since $\lim_{x \to 2^{-}} f(x) \ne \lim_{x \to 2^{+}} f(x)$; rem b) discontinuous since $f(2)$ DNE; non-rem c) discontinuous since $\lim_{x \to 2} f(x)$ DNE, non-rem. d) continuous 4. $f(x) = \begin{cases} 3x - 7, & x \le 1 \\ -x + 2, & x > 1 \end{cases}; c = 1$ a) continuous b) discontinuous since $f(1)$ DNE; rem c) discontinuous since $\lim_{x \to 1} f(x) \ne f(1)$; rem d) discontinuous since $\lim_{x \to 1^{-}} f(x) \ne \lim_{x \to 1^{+}} f(x)$; non-rem

          3.
$f(x) = \begin{cases} 3x - 1, & x < 2 \\ x + 3, & x \ge 2 \end{cases}; c = 2$
a) discontinuous since $\lim_{x \to 2^{-}} f(x) \ne \lim_{x \to 2^{+}} f(x)$; rem
b) discontinuous since $f(2)$ DNE; non-rem
c) discontinuous since $\lim_{x \to 2} f(x)$ DNE, non-rem. d) continuous
4.
$f(x) = \begin{cases} 3x - 7, & x \le 1 \\ -x + 2, & x > 1 \end{cases}; c = 1$
a) continuous
b) discontinuous since $f(1)$ DNE; rem
c) discontinuous since $\lim_{x \to 1} f(x) \ne f(1)$; rem
d) discontinuous since $\lim_{x \to 1^{-}} f(x) \ne \lim_{x \to 1^{+}} f(x)$; non-rem

3.
f(x) = 3x - 1, x < 2
x + 3, x ≥ 2 ; c = 2
a) discontinuous since limx → 2^- f(x) limx → 2^+ f(x); rem
b) discontinuous since f(2) DNE; non-rem
c) discontinuous since limx → 2 f(x) DNE, non-rem. d) continuous
4.
f(x) = 3x - 7, x ≤ 1
-x + 2, x > 1 ; c = 1
a) continuous
b) discontinuous since f(1) DNE; rem
c) discontinuous since limx → 1 f(x) f(1); rem
d) discontinuous since limx → 1^- f(x) limx → 1^+ f(x); non-rem

Added by Jason W.

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