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)
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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.
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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.
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