MATHEMATICAL METHODS ASSIGNMENT SENIOR HIGH SCHOOL 2 MM2.04 POLYNOMIALS (60 point) SMAK BPK PENABUR SINGGASANA ACADEMIC YEAR 2024/2025 Due date : 14 October 2024 Name/Class : / Section A. Chose the one you consider correct. 1. The graph of the function 𝑓 passes through the point (−2,7). 𝑥 If ℎ (𝑥 ) = 𝑓 (2 ) + 5, then the graph of the function ℎ must pass through the point 2. A. (−1, −12) B. (−1,19) C. (−4, −12) D. (−4,12) E. (−1,12) The point 𝐴(3,2) lies on the graph of the function 𝑓. A transformation maps the 1 graph of 𝑓 to the graph of 𝑔, where 𝑔(𝑥 ) = 𝑓(𝑥 − 1). The same transformation 2 maps the point 𝐴 to the point 𝑃. The coordinates of the point 𝑃 are A. (2,1) B. (2,4) C. (4,1) D. (4,2) E. (4,4) Section B. Answer the following questions correctly. 3. Let 𝑓 ∶ 𝑅 → 𝑅, 𝑓(𝑥 ) = 𝑥 2 − 4 and 𝑔 ∶ 𝑅 → 𝑅, 𝑔(𝑥 ) = 4(𝑥 − 1)2 − 4. Let the graph of ℎ be a transformation of the graph of 𝑓 where the transformations have been applied in the following order: • 1 dilation by a factor of 2 from the vertical axis (parallel to the horizontal axis) • translation by two units to the right (in the direction of the positive horizontal axis) State the rule of ℎ and coordinates of the horizontal axis intercepts of the graph of ℎ. (2 mark) EE/MM/09/10/24 P a g e |1 4. 1 Let 𝑓 ∶ 𝑅 → 𝑅, 𝑓(𝑥 ) = 4 (𝑥 + 2)2 (𝑥 − 2)2 and 1 ℎ ∶ 𝑅 → 𝑅, ℎ(𝑥 ) = − 4 (𝑥 + 2)2 (𝑥 − 2)2 + 2. Part of the graphs of 𝑓 and ℎ are shown below. Write a sequence of two transformations that map the graph of 𝑓 onto the graph of ℎ. (1 mark) • • 5. The function 𝑓 ∶ 𝑅 → 𝑅, 𝑓 (𝑥 ) is a polynomial function of degree 4. Part of the graph of 𝑓 is shown below. The graph of 𝑓 touches the 𝑥-axis at the origin. Find the rule of 𝑓. EE/MM/09/10/24 P a g e |2 6. 1 Let 𝑓 ∶ 𝑅 → 𝑅, 𝑓(𝑥 ) = 2𝑥 + 𝑥 and 𝑔 ∶ 𝑅 → 𝑅, 𝑔(𝑥 ) = (2 − 𝑥). 2 Complete a possible sequence of transformations to map 𝑓 to 𝑔. • (2 mark) 1 Dilation of factor 2 from the 𝑥-axis. • • 7. 𝜋 Determine the transformation that map 𝑦 = sin 𝑥 onto 𝑦 = sin (𝑥 − 4 ) Section C. Jawablah setiap pertanyaan berikut. 8. Diberikan fungsi 𝑓 (𝑥 ) = 𝑥 3 − 22𝑥 2 + 163𝑥 + 404. (a) Buktikan bahwa fungsi 𝑓 tidak memiliki akar rasional menggunakan Rational Root Theorem. (b) Gunakan bisection method untuk menentukan nilai 𝑥. 9. Diberikan fungsi 𝑓 (𝑥 ) = 𝑥 2 − 𝑏𝑥 + 36. Tentukan nilai 𝑏 sehingga fungsi 𝑓 memiliki akar rasional. 10. Diberikan fungsi 𝑓 (𝑥 ) = 𝑥 2 − 8𝑥 + 𝑐. Tentukan nilai 𝑐 sehingga fungsi 𝑓 memiliki akar rasional. EE/MM/09/10/24 P a g e |3