1. For the first graph:
- Vertex: (2, 1)
- Axis of symmetry: x = 2
- Domain: All real numbers
- Range: y ≥ 1
- Increasing on: (2, ∞)
- Decreasing on: (-∞, 2)
- x-intercepts: None
- y-intercept: (0, 5)
- End behavior: As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞
2. For the second graph:
- Vertex: (0, 0)
- Axis of symmetry: x = 0
- Domain: All real numbers
- Range: y ≥ 0
- Increasing on: (0, ∞)
- Decreasing on: (-∞, 0)
- x-intercepts: (0, 0)
- y-intercept: (0, 0)
- End behavior: As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞
3. For the third graph:
- Vertex: (-1, -4)
- Axis of symmetry: x = -1
- Domain: All real numbers
- Range: y ≥ -4
- Increasing on: (-1, ∞)
- Decreasing on: (-∞, -1)
- x-intercepts: (-3, 0) and (1, 0)
- y-intercept: (0, -3)
- End behavior: As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞
4. For the fourth graph:
- Vertex: (0, 3)
- Axis of symmetry: x = 0
- Domain: All real numbers
- Range: y ≤ 3
- Increasing on: (-∞, 0)
- Decreasing on: (0, ∞)
- x-intercepts: (-2, 0) and (2, 0)
- y-intercept: (0, 3)
- End behavior: As x → ∞, f(x) → -∞; As x → -∞, f(x) → -∞
Parent Tip: Review the logic above to help your child master the concept of features of functions worksheet answers.
