1) f(x) = (1 - x) (1 - 3x)
| x | -∞ 1/3 1 +∞ |
| 1 - x | + | + 0 - |
| 1 - 3x | + 0 - | - |
| f(x) | + 0 - 0 + |
2) f(x) = (2x + 5)² (x + 3)
| x | -∞ -5/2 3 +∞ |
| 2x + 5 | - 0 + | + |
| 2x + 5 | - 0 + | + |
| x - 3 | - | - 0 + |
| f(x) | - 0 - 0 + |
3) f(x) = x(2x - 3) (3x - 4)
| x | -∞ 0 4/3 3/2 +∞ |
| x | - 0 + | + | + |
| 2x - 3 | - | - | - 0 + |
| 3x - 4 | - | - 0 + | + |
| f(x) | - 0 + 0 - 0 + |
4) f(x) = (x + √2) (√2 x + 1)
| x | -∞ -√2 -√2/2 +∞ |
| x + √2 | - 0 + | + |
| √2 x + 1 | - | - 0 + |
| f(x) | + 0 - 0 + |
5) f(x) = x/(x + 1)
| x | -∞ -1 0 +∞ |
| x | - | - 0 + |
| x + 1 | - 0 + | + |
| f(x) | + || - 0 + |
6) f(x) = 1/(3x(x - 4))
| x | -∞ 0 4 +∞ |
| 1 | + | + | + |
| 3x | - 0 + | + |
| x - 4 | - | - 0 + |
| f(x) | + || - || + |
7) f(x) = (x² - 4)/(x + 1)
| x | -∞ -2 -1 2 +∞ |
| x - 2 | - | - | - 0 + |
| x + 2 | - 0 + | + | + |
| x + 1 | - | - 0 + | + |
| f(x) | - 0 + || - 0 + |
8) f(x) = (x - 3x²)/(x²(5 - x)
| x | -∞ 0 1/3 5 +∞ |
| x | - 0 + | + | + |
| 1 - 3x | + | + 0 - | - |
| x² | + 0 + | + | + |
| 5 - x | + | + | + 0 - |
| f(x) | - || + 0 - || + |
9) f(x) = x - 3/???
10) f(x) = (1/x) : 1/(x + 5)
| x | -∞ -5 0 +∞ |
| x | - | - 0 + |
| x + 5 | - 0 + | + |
| f(x) | + || - || + |