1 Grade 11 Functions Chapter 3 Assignment Name:______________________________ K: /10 T: /5 C: /5 A: /10 1. [K5] For each function f(x), determine the equation for the appropriate g(x). a) f(x) = 1/x...

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1 Grade 11 Functions Chapter 3 Assignment Name:______________________________ K: /10 T: /5 C: /5 A: /10 1. [K5] For each function f(x), determine the equation for the appropriate g(x). a) f(x) = 1/x g(x) = f(x – 1) + 2 b) f(x) = √x g(x) = 4f(3x) c) f(x) = x g(x) = -5f(x) - 3 d) f(x) = x 2 g(x) = -2f[3(x – 4)] e) f(x) = √x g(x) = f(x + 3) + 5 2. [C5] Show the following set of ordered pairs in a mapping diagram. Is the relation a function? Justify your answer. (-5, 6), (-4, 9), (-3, 1), (-5, -6), (1, -2), (3, 8), (8, 8) 2 3. [A5] Determine the inverse of the function f(x) = -x + 5 and sketch it below. 2 4–2–4 x 2 4 –2 –4 y 4. [K5] For each function f(x), determine the equation for the appropriate g(x). a) f(x) = (x + 1) 2 + 4 g(x) = f(-x) b) f(x) = -4 + √(x + 4) g(x) = -f(x) c) f(x) = (x + 5) 2 – 8 g(x) = -f(-x) d) f(x) = 6 + (1/[x +3]) g(x) = f(-x) 3 e) f(x) = -1 + √(x + 9) g(x) = -f(-x) 5. [T5] The speed of a tsunami (or tidal wave) depends on the depth of the water and can be calculated using the formula v(h) = √(9.8h), where h is the depth of the water, in metres. (a) Sketch the graph of this function below; (b) determine the speed of a tsunami at a depth of 2m; (c) determine the speed of a tsunami at a depth of 4000m; (d) state the domain and range of the tsunami speed function. 2 4–2–4 x 2 4 –2 –4 y 6. [A5] If f(x) = 1/x, determine the function g(x), where g(x) = f(x + 2) + 4. Then sketch g(x) below. 2 4–2–4 x 2 4 –2 –4 y