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IB Mathematics: Applications and Interpretation SL · 12.5: Functions · 12.5.6

Functions: exam review Exam review Answers

Section A: short questions

    1. (a) (2, 7.39)
    2. (b) (7.39, 2)
    3. (c) 2
    4. (d) They are inverse functions: the graph of g is the reflection of the graph of f in y = x
    1. (a) x = 2 and y = 5
    2. (b) b = 3, c = 4
    3. (c) \(f(x)\ne 5\)
    1. (a) (0.5, 3.16)
    2. (b) B is (3.16, 0.5); mirror line y = x
    3. (c) 0.500
    1. (a) t = −3 and N = 450
    2. (b) The number of members gets close to 450 but never reaches or passes it.
    3. (c) 300
    1. (a) C(40) = 16.50; n = 60
    2. (b) 0 ≤ n ≤ 120, n a whole number; 2.5 ≤ C ≤ 44.50
    3. (c) x ≥ 4; g(x) ≥ 3
    4. (d) −4 ≤ h(x) ≤ 5

Section B: long questions

    1. (a) As t increases, k^(−t) tends to 0, so D tends to a; a is the total distance
    2. (b) b = −18
    3. (c) k = 1.43
    4. (d) 6.17 km
    5. (e) 8.10 hours
    1. (a) As t increases, \(k^{-t}\) tends to 0, so D tends to a; a = 45
    2. (b) b = −45
    3. (c) k = 1.80
    4. (d) 7.72 km
    5. (e) 8 hours
    1. (a) y-intercept −60; zeros x = 2 and x = 10; vertex (6, 48); the greatest profit is 48 euros, made at a price of 6 euros
    2. (b) T = 22; the temperature falls towards but never goes below 22 °C (the temperature of the kitchen); 94.4 °C
    3. (c) a = 200; N = 50; as p tends to 0, N grows without limit, so the graph never meets the N-axis (a price of 0 gives no value of N)
    4. (d) C(0) = 12; n = −5 and C = 4
    5. (e) Exponential; each value is 2 times the one before

jmaths.xyz · AI SL · 12.5.6 Unit review