Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook suitable for SPM (Add Maths) too

1. analytical method 解析法
Venn diagrams 范氏图示法
tabulation method 列表法
graphical method 图象法

2. 𝒑𝒈 𝟏𝟎
𝒇 𝒙 = ? 𝒙
Venn diagrams 范氏图示法
𝒇 𝒂 = 𝒃
𝒇 𝒙 = 𝒙𝟐
+ 𝟏
𝒇 𝒙 = 𝟐𝒙 + 𝟐 𝒇 𝒙 =
𝒙
𝒙 + 𝟏
𝒇 𝒙 = 𝒙𝟐

3. analytical method 解析法
Venn diagrams 范氏图示法
tabulation method 列表法
graphical method 图象法

4. 𝒑𝒈 𝟖, 𝟗 analytical method 解析法
𝒏 < 𝒙 ≤ 𝒏 + 𝟏 (𝒏 𝝐 𝑵, 𝒏 ≥ 𝟏𝟎)
𝑵 = 𝒏𝒂𝒕𝒖𝒓𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 = 𝟏, 𝟐, 𝟑, 𝟒 …
graphical method 图象法

5. 𝒑𝒈 𝟐𝟔 analytical method 解析法
graphical method 图象法
analytical method 解析法
𝒚 =
𝟐 𝟎 < 𝒙 ≤ 𝟐𝟎
图象法
graphical method
𝟒 𝟐𝟎 < 𝒙 ≤ 𝟒𝟎
𝟔 𝟒𝟎 < 𝒙 ≤ 𝟔𝟎

6. 𝒑𝒈 𝟏𝟏 analytical method 解析法
graphical method 图象法
analytical method 解析法
𝒚 =
𝒙, 𝟎 < 𝒙 ≤ 𝟏𝟎
𝟐 + 𝟎. 𝟖𝒙, 𝟏𝟎 < 𝒙 ≤ 𝟐𝟎
≤ 𝟏𝟎 𝒌𝒈, 𝒔𝒆𝒍𝒍𝒊𝒏𝒈 𝒑𝒓𝒊𝒄𝒆 𝒐𝒇 𝒙 𝒌𝒈 = 𝟏𝒙
> 𝟏𝟎 𝒌𝒈, 𝒔𝒆𝒍𝒍𝒊𝒏𝒈 𝒑𝒓𝒊𝒄𝒆 𝒐𝒇 𝒙 𝒌𝒈 = 𝟏𝟎 + 𝟎. 𝟖 𝒙 − 𝟏𝟎
= 𝟏𝟎 + 𝟎. 𝟖𝒙 − 𝟖
= 𝟐 + 𝟎. 𝟖𝒙
图象法
graphical method

7. 𝒑𝒈 𝟏𝟎 analytical method 解析法
𝒇 𝒏 = 𝟑𝒏 − 𝟐 (𝒏 𝝐 𝑵)
𝒇 𝒂 = 𝒃
𝒈 𝒙 = 𝟓𝒙𝟐 (𝒙 𝝐 𝑹)
𝒉 𝒙 = 𝟏 (𝒙 𝝐 + 𝒗𝒆 𝑹) 𝒉 𝒙 = −𝟏 (𝒙 𝝐 − 𝒗𝒆 𝑹) 𝒉 𝟎 = 𝟎 (𝒙 𝝐 𝑹)
𝒉 𝒙 =
𝟏, 𝒙 > 𝟎 时
0, 𝒙 = 𝟎 时
−𝟏, 𝒙 < 𝟎 时
R, x ≠ 0 mapped to its reciprocal
(a number that when multiplied by a
given number gives one as a product)
𝒌 𝒙 =
𝟏
𝒙
(𝒙 𝝐 𝑹, 其 𝒙 ≠ 𝟎)

8. 𝒑𝒈 𝟏𝟎 analytical method 解析法
graphical method 图象法

9. 𝒑𝒈 𝟏𝟎 graphical method 图象法

10. 𝒑𝒈 𝟏𝟎 graphical method 图象法

11. 𝒑𝒈 𝟏𝟎 graphical method 图象法 𝒑𝒈 𝟏𝟏 graphical method 图象法
𝟏𝟓 °𝑪, 𝟏𝟒 时
− 𝟓 °𝑪, 𝟐 时

12. analytical method 解析法
Venn diagrams 范氏图示法
tabulation method 列表法
graphical method 图象法

13. 𝒑𝒈 𝟏𝟏 analytical method 解析法
tabulation method 列表法
𝑻 =
−𝟑
𝟓𝟎𝟎
𝒉 + 𝟏𝟎 𝟏 °𝑪
原象
𝒑𝒓𝒆𝒊𝒎𝒂𝒈𝒆 𝒇 𝒂 = 𝒃
𝑻𝟎 = ? 𝒉 + 𝟏𝟎 = 𝟏𝟎
𝑻𝟓𝟎𝟎 =
𝑻𝟓𝟎𝟎−𝑻𝟎
𝒉𝟓𝟎𝟎−𝒉𝟎
(𝟓𝟎𝟎) + 𝟏𝟎 = 𝟕
𝑻𝟓𝟎𝟎 =
−𝟑
𝟓𝟎𝟎
(𝟓𝟎𝟎) + 𝟏𝟎 = 𝟕
𝑻𝟏𝟎𝟎𝟎 =
−𝟑
𝟓𝟎𝟎
(𝟏𝟎𝟎𝟎) + 𝟏𝟎 = 𝟒
𝑻𝟐𝟎𝟎𝟎 =
−𝟑
𝟓𝟎𝟎
(𝟐𝟎𝟎𝟎) + 𝟏𝟎 = −𝟐
𝑻𝟑𝟎𝟎𝟎 =
−𝟑
𝟓𝟎𝟎
(𝟑𝟎𝟎𝟎) + 𝟏𝟎 = −𝟖
𝑻𝟏𝟓𝟎𝟎 =
−𝟑
𝟓𝟎𝟎
𝟏𝟓𝟎𝟎 + 𝟏𝟎 = 𝟏
𝑻𝟏𝟓𝟎𝟎 =
𝑻𝟏𝟎𝟎𝟎 + 𝑻𝟐𝟎𝟎𝟎
𝟐
= 𝟏
−𝟑 −𝟔
+𝟓𝟎𝟎 +𝟏𝟎𝟎𝟎