1. f(x) = (x² - 4)/(x² - 9)
Points of discontinuity: x = -3, x = 3
Holes: none
x-intercept: (-2, 0), (2, 0)
y-intercept: (0, 4/9)
Horizontal asym: y = 1
Domain: (-∞, -3) ∪ (-3, 3) ∪ (3, ∞)
Limit behavior of all vertical asym:
As x → -3⁻, f(x) → ∞; as x → -3⁺, f(x) → -∞
As x → 3⁻, f(x) → -∞; as x → 3⁺, f(x) → ∞
End behavior asym: y = 1
2. f(x) = (x² - x - 6)/(x² - 2x - 8)
Points of discontinuity: x = -2, x = 4
Holes: at x = -2 (point (-2, 5/6))
x-intercept: (3, 0)
y-intercept: (0, 3/4)
Horizontal asym: y = 1
Domain: (-∞, -2) ∪ (-2, 4) ∪ (4, ∞)
Limit behavior of all vertical asym:
As x → 4⁻, f(x) → -∞; as x → 4⁺, f(x) → ∞
End behavior asym: y = 1
Parent Tip: Review the logic above to help your child master the concept of graphing rational functions worksheet.
