Graffiau ciwbig – Uwch yn unig
Graff ciwbig yw unrhyw graff sydd â \(\text{x}^3\) yn ei hafaliad. Mae graffiau ciwbig yn dal i fod ar ffurf cromlin ond maen nhw’n gallu bod â mwy nag un newid cyfeiriad ynddyn nhw.
Enghraifft
Gad i ni lunio graff \(\text{y = x}^3-\text{x~+~8}\). Yn gyntaf, mae angen i ni gwblhau ein tabl gwerthoedd:
| \(\text{x}\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| \(\text{y = x}^3-\text{x~+~8}\) |
| \(\text{x}\) |
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(\text{y = x}^3-\text{x~+~8}\) |
- pan fo \(\text{x}\) = -3, \(\text{y}\) = (-3 × -3 × -3) – (-3) + 8 = -16
- pan fo \(\text{x}\) = -2, \(\text{y}\) = (-2 × -2 × -2) – (-2) + 8 = 2
- pan fo \(\text{x}\) = -1, \(\text{y}\) = (-1 × -1 × -1) – (-1) + 8 = 8
- pan fo \(\text{x}\) = 0, \(\text{y}\) = (0 × 0 × 0) – 0 + 8 = 8
- pan fo \(\text{x}\) = 1, \(\text{y}\) = (1 × 1 × 1) – 1 + 8 = 8
- pan fo \(\text{x}\) = 2, \(\text{y}\) = (2 × 2 × 2) – 2 + 8 = 14
- pan fo \(\text{x}\) = 3, \(\text{y}\) = (3 × 3 × 3) – 3 + 8 = 32
| \(\text{x}\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| \(\text{y = x}^3-\text{x~+~8}\) | -16 | 2 | 8 | 8 | 8 | 14 | 32 |
| \(\text{x}\) |
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(\text{y = x}^3-\text{x~+~8}\) |
| -16 |
| 2 |
| 8 |
| 8 |
| 8 |
| 14 |
| 32 |
Yna bydd y graff yn edrych fel hyn:
Question
Cwblha’r tabl a llunia graff \(\text{y = x}^3+\text{x}^2-\text{12}\).
| \(\text{x}\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| \(\text{y = x}^3+\text{x}^2-\text{12}\) |
| \(\text{x}\) |
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(\text{y = x}^3+\text{x}^2-\text{12}\) |
| \(\text{x}\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| \(\text{y = x}^3+\text{x}^2-\text{12}\) | -30 | -16 | -12 | -12 | -10 | 0 | 24 |
| \(\text{x}\) |
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(\text{y = x}^3+\text{x}^2-\text{12}\) |
| -30 |
| -16 |
| -12 |
| -12 |
| -10 |
| 0 |
| 24 |