Podcast
Questions and Answers
What is the function for a linear function?
What is the function for a linear function?
f(x) = x
What is the range of a quadratic function?
What is the range of a quadratic function?
(0, ∞)
What is the domain of a reciprocal function?
What is the domain of a reciprocal function?
(-∞, 0) ∪ (0, ∞)
The range of an absolute value function is ______.
The range of an absolute value function is ______.
The range of the sine function is [-1, 1].
The range of the sine function is [-1, 1].
Which function has a domain of (0, ∞)?
Which function has a domain of (0, ∞)?
What is the function for a cubic equation?
What is the function for a cubic equation?
What is the range of an exponential function?
What is the range of an exponential function?
The domain of the tangent function is ______.
The domain of the tangent function is ______.
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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]
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