(2) Determine if each function is continuous at the given value of a. Justify your answers using limits and the definition of continuity. If any functions are NOT continuous at a, determine which properties of continuity are satisfied and which properties fail. 12 – 4r +3 (a) f(r) at a = 3. I-3

College Algebra (MindTap Course List)
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Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
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I need help answering question #2

(2) Determine if each function is continuous at the given value of a. Justify your answers using
limits and the definition of continuity. If any functions are NOT continuous at a, determine
which properties of continuity are satisfied and which properties fail.
1² – 4r + 3
(a) f(r) =
at a = 3.
T - 3
12 – 4r + 3
if r +3
(b) g(x)
T - 3
at a = 3.
if r = 3
(c) For the function g(r) in part (c), how would you "remove the discontinuity"? In other
words, how could you re-define g(r) in order to make it continuous at a = 3? Be sure to
write your new function g(r).
Transcribed Image Text:(2) Determine if each function is continuous at the given value of a. Justify your answers using limits and the definition of continuity. If any functions are NOT continuous at a, determine which properties of continuity are satisfied and which properties fail. 1² – 4r + 3 (a) f(r) = at a = 3. T - 3 12 – 4r + 3 if r +3 (b) g(x) T - 3 at a = 3. if r = 3 (c) For the function g(r) in part (c), how would you "remove the discontinuity"? In other words, how could you re-define g(r) in order to make it continuous at a = 3? Be sure to write your new function g(r).
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