- Constant Function: f(x) = c; Parent Function: f(x) = 0; Graph: Horizontal line at y = c; Characteristics: Domain: All real numbers, Range: {c}, No x-intercept (unless c=0), y-intercept: (0,c), Symmetry: Even function, Asymptotes: None, End Behavior: y → c as x → ±∞, Rate of Change: 0.
- Linear or Identity Function: f(x) = x; Parent Function: f(x) = x; Graph: Straight line through origin with slope 1; Characteristics: Domain: All real numbers, Range: All real numbers, x-intercept: (0,0), y-intercept: (0,0), Symmetry: Odd function, Asymptotes: None, End Behavior: y → ∞ as x → ∞, y → -∞ as x → -∞, Rate of Change: 1.
- Quadratic Function: f(x) = x²; Parent Function: f(x) = x²; Graph: Parabola opening upwards with vertex at origin; Characteristics: Domain: All real numbers, Range: [0, ∞), x-intercept: (0,0), y-intercept: (0,0), Symmetry: Even function, Asymptotes: None, End Behavior: y → ∞ as x → ±∞, Rate of Change: 2x.
- Square Root Function: f(x) = √x; Parent Function: f(x) = √x; Graph: Curve starting at origin and increasing to the right; Characteristics: Domain: [0, ∞), Range: [0, ∞), x-intercept: (0,0), y-intercept: (0,0), Symmetry: Neither even nor odd, Asymptotes: None, End Behavior: y → ∞ as x → ∞, Rate of Change: 1/(2√x).
Parent Tip: Review the logic above to help your child master the concept of parent functions worksheet.
