Function Types and Properties Quiz

Study Notes

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]

Description

Test your knowledge on different types of functions, including linear, quadratic, cubic, absolute value, reciprocal, exponential, and logarithmic functions. This quiz covers their domains and ranges, essential for understanding functional behavior in mathematics.