Function Types and Properties Quiz

Linear Function

• Defined by f(x) = x
• Both domain and range are all real numbers: (-∞, ∞)

Quadratic Function

• Expressed as f(x) = x²
• Domain includes all real numbers: (-∞, ∞)
• Range is non-negative real numbers: (0, ∞)

Cubic Function

• Formulated as f(x) = x³
• Domain covers all real numbers: (-∞, ∞)
• Range also spans all real numbers: (-∞, ∞)

Absolute Value Function

• Represented by f(x) = |x|
• Domain consists of all real numbers: (-∞, ∞)
• Range includes only non-negative values: [0, ∞)

Reciprocal Function

• Defined as f(x) = 1/x
• Domain excludes zero: (-∞, 0) ∪ (0, ∞)
• Range excludes zero as well: (-∞, 0) ∪ (0, ∞)

Exponential Function

• Given by f(x) = e^x
• Domain encompasses all real numbers: (-∞, ∞)
• Range includes positive real numbers: (0, ∞)

Logarithmic Function

• Expressed as f(x) = ln(x)
• Domain starts from zero and includes positive numbers: (0, ∞)
• Range includes all real numbers: (-∞, ∞)

Square Root Function

• Formulated as f(x) = √x
• Domain consists of non-negative real numbers: [0, ∞)
• Range includes non-negative real numbers: [0, ∞)

Tangent Function

• Defined by f(x) = tan(x)
• Domain excludes odd multiples of π/2: (-∞, π/2) ∪ (π/2, 3π/2) ∪ (3π/2, ∞)
• Range encompasses all real numbers: (-∞, ∞)

Sine Function

• Represented as f(x) = sin(x)
• Domain encompasses all real numbers: (-∞, ∞)
• Range is limited to [-1, 1]

Cosine Function

• Expressed by f(x) = cos(x)
• Domain covers all real numbers: (-∞, ∞)
• Range is also limited to [-1, 1]