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KEY CONCEPT Now, if a function is given without its corresponding graph, we must find other means to determine if the function is continuous or not on an interval. EXAMPLE 3: Determine the largest interval over which the functions f(x) = vx + 5 is continuous. Solution: Observe that the function f(x) = vx + 5 has function values only if x + 5 2 0, that is, if x E [-5,co). For all c E (-5,00), f(c) = Vc + 5 = lim vx + 5. Moreover, f is continuous from the right at -5 because f(-5) = 0 = lim vx +5. x-+-5 Therefore, for all x E [-5, co), the function f(x) = vx + 5 is continuous. Starter 2: The Largest the Best (Illustrating continuity of a function on an interval) Directions: Do this activity with your groupmates with 3 members. Match Column A (Set of Functions) with Column B (Largest Intervals). Column A Column B 1. f (x) = Vx a. [-,00) 2. g(x) = Vx +3 b. [0,00) 3. h(x) = Vx -6 c. (-00,= ] 4. g(x) = VI + 2x d. [6, 00) 5. f (x) = V3 - 4x e. [-3,00) KEY CONCEPT EXAMPLE 4: Determine the largest interval over which g(x) = is continuous. Solution: Observe that the given rational function g(x) = = is not defined at x = 2 and x = -2. Hence, the domain of g is the set R \\ {-2, 2). As mentioned at the start of this topic, a rational function is continuous on its domain. Hence, g is continuous over R \\ {-2,21. REINFORCER(DYAD) Guided Practice 1: Am I Real? (Illustrating continuity of a function on an interval) Directions: Do this activity with a partner. Match Column A (Set of Functions) with Column B (Largest Intervals). Column A Column B 1. f(x) =_ a. R \\ (-2,-1) 2. g(x) = 3-25 b. R \\ {-1,1) 3. h(x) = x+2 x343x+2 C. R \\ (4,7} x-5 4. g(x) = 3-11x+28 d. R \\(-=.4) 5. f(x) = = 9-X 5x3-17x-12 e. R\\ {-5,5)