A Library of Parent Functions

The Constant Parent Function

• Equation: f(x) = c• Domain: (-∞,∞)• Range: [c]• Increasing: None• Decreasing: None• Constant: (-∞,∞)• Symmetry: y-axis

The Linear Parent Function (Identity)

• Equation: f(x) = x• Domain: (-∞,∞)• Range: (-∞,∞)• Increasing: (-∞,∞)• Decreasing: None• Constant: None• Symmetry: Origin

The Absolute Value Parent Function

• Equation: f(x)• Domain: (-∞,∞)• Range: [0,∞)• Increasing: (0,∞)• Decreasing: (-∞,0) • Constant: None• Symmetry: y-axis

The Quadratic Parent Function (Squaring)

• Equation: f(x)x2

• Domain: (-∞,∞)• Range: [0,∞)• Increasing: (0,∞)• Decreasing: (-∞,0) • Constant: None• Symmetry: y-axis

The Cubic Parent Function

• Equation: f(x) = x3

• Domain: (-∞,∞)• Range: (-∞,∞)• Increasing: (-∞,∞)• Decreasing: None• Constant: None• Symmetry: Origin

The Square Root Parent Function

• Equation: f(x)• Domain: [0,∞)• Range: [0,∞)• Increasing: (0,∞)• Decreasing: None• Constant: None• Symmetry: None

The Reciprocal Parent Function (Rational, Inverse)

• Equation: f(x) = • Domain: (-∞,0)U(0, ∞)• Range: (-∞,0)U(0, ∞)• Increasing: None• Decreasing: (-∞,0)U(0, ∞)• Constant: None• Symmetry: Origin

The Exponential Parent Function

• Equation: f(x) = 2x

• Domain: (-∞,∞)• Range: (0,∞)• Increasing: (-∞,∞)• Decreasing: None• Constant: None• Symmetry: None