MS-MHFU Unit 2 Test Rational Functions PDF Past Paper

Unit 2 Test : Rational Functions General marking notations: M : marks for method A : marks for application R : marks for reasoning N : marks when no working shown, but answer is correct. (No M,A,R marks will be provided in this case. Only the marks indicated with N will be awarded 1....

Unit 2 Test : Rational Functions General marking notations: M : marks for method A : marks for application R : marks for reasoning N : marks when no working shown, but answer is correct. (No M,A,R marks will be provided in this case. Only the marks indicated with N will be awarded 1. 3 a) 1 A1 t+4 40 −1>0 A1 t+4 Make the denominator common: R1 40−(t+4) >0 A2 t+4 −(t−36) >0 A1 t+4 t−36 0 so, the domain is: R1 0 < t < 36 A1 𝑡 ∈ (0,36) A1 3. a) As we have a vertical asymptote at 𝑥 = −1, the denominator will be (𝑥 + 1).R1M1A1 As we have x-intercept as 𝑥 = 2, the numerator will have (𝑥 − 2). R1M1A1 1 As we have a horizontal asymptote at 𝑦 = − 2, the coefficient of numerator will be 1 − 2 times that of denominator. R1M1A1 So, the equation for the function becomes: 1 𝑥−2 𝑓(𝑥) = − 2. 𝑥+1 R1M1A1 b) Yes, it is. possible to have another function with same key features as we get an exact function dependent of some other variable-restriction for these key features. There is no other constant whose value needs to be ascertained further. R2M3