1. y = 1/(x + 2)
- x-intercepts: None
- Vertical Asymptotes: x = -2
- Horizontal or Slant Asymptotes: y = 0
- Holes: None
- y-Intercept(s): (0, 1/2)
- Domain: All real numbers except x = -2
- Range: All real numbers except y = 0
2. y = (x² + 5x + 6)/(x² - 9)
- x-intercepts: x = -2
- Vertical Asymptotes: x = 3
- Horizontal or Slant Asymptotes: y = 1
- Holes: (x = -3, y = 1/3)
- y-Intercept(s): (0, -2/3)
- Domain: All real numbers except x = 3 and x = -3
- Range: All real numbers except y = 1
3. y = (x² - 4)/(3x² - 15x + 18)
- x-intercepts: x = -2
- Vertical Asymptotes: x = 3
- Horizontal or Slant Asymptotes: y = 1/3
- Holes: (x = 2, y = 2/3)
- y-Intercept(s): (0, -2/9)
- Domain: All real numbers except x = 3 and x = 2
- Range: All real numbers except y = 1/3
4. y = 5/(x - 2)²
- x-intercepts: None
- Vertical Asymptotes: x = 2
- Horizontal or Slant Asymptotes: y = 0
- Holes: None
- y-Intercept(s): (0, 5/4)
- Domain: All real numbers except x = 2
- Range: All real numbers greater than 0 (y > 0)
Parent Tip: Review the logic above to help your child master the concept of graphing rational functions worksheet.