Function Types and Properties Quiz

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Questions and Answers

What is the function for a linear function?

f(x) = x

What is the range of a quadratic function?

(0, ∞)

What is the domain of a reciprocal function?

(-∞, 0) ∪ (0, ∞)

The range of an absolute value function is ______.

<p>[0, ∞)</p> Signup and view all the answers

The range of the sine function is [-1, 1].

<p>True (A)</p> Signup and view all the answers

Which function has a domain of (0, ∞)?

<p>Logarithmic (C)</p> Signup and view all the answers

What is the function for a cubic equation?

<p>f(x) = x³ (A)</p> Signup and view all the answers

What is the range of an exponential function?

<p>(0, ∞)</p> Signup and view all the answers

The domain of the tangent function is ______.

<p>(-∞, π/2) ∪ (π/2, 3π/2) ∪ (3π/2, ∞)</p> Signup and view all the answers

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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 Ï€/2: (-∞, Ï€/2) ∪ (Ï€/2, 3Ï€/2) ∪ (3Ï€/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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