Basic Functions and Graphs Flashcards

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Questions and Answers

What is the equation for the Identity Function?

  • y = 1/x
  • y = √x
  • y = x (correct)
  • y = x^2

What is the range of The Squaring Function?

[0,∞)

The Cubing Function has any discontinuities.

False (B)

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

<p>The Reciprocal Function (C)</p> Signup and view all the answers

What type of symmetry does The Absolute Value Function have?

<p>Even</p> Signup and view all the answers

What is the range of The Exponential Function?

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

The Natural Log Function has a vertical asymptote at x=0.

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

What is the bounded condition of The Sine Function?

<p>Bounded or BOTH @ y=1 &amp; y=-1 (D)</p> Signup and view all the answers

What is the equation for The Logistic Function?

<p>y = 1/(1+e^-x)</p> Signup and view all the answers

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Study Notes

Identity Function

  • Formula: y = x
  • Domain: All real numbers
  • Range: All real numbers
  • No discontinuities; strictly increasing
  • Displays odd symmetry around the origin
  • Unbounded both above and below

Squaring Function

  • Formula: y = x²
  • Domain: All real numbers
  • Range: [0, ∞)
  • Decreasing on the interval (-∞, 0], increasing on [0, ∞)
  • Displays even symmetry across the y-axis
  • Bounded below at y=0

Cubing Function

  • Formula: y = x³
  • Domain: All real numbers
  • Range: All real numbers
  • No discontinuities; strictly increasing
  • Displays odd symmetry around the origin
  • Unbounded in both directions

Reciprocal Function

  • Formula: y = 1/x
  • Domain: (-∞, 0) ∪ (0, ∞)
  • Range: (-∞, 0) ∪ (0, ∞)
  • Discontinuity at x=0 (vertical asymptote)
  • Decreasing on (-∞, 0) and increasing on (0, ∞)
  • Displays odd symmetry around the origin
  • Not bounded

Square Root Function

  • Formula: y = √x
  • Domain: [0, ∞)
  • Range: [0, ∞)
  • No discontinuities; strictly increasing
  • No symmetry
  • Bounded below at y=0

Absolute Value Function

  • Formula: y = |x|
  • Domain: All real numbers
  • Range: [0, ∞)
  • Decreasing on (-∞, 0] and increasing on [0, ∞)
  • Displays even symmetry across the y-axis
  • Bounded below at y=0

Greatest Integer Function

  • Formula: y = int(x)
  • Domain: All real numbers
  • Range: Integer values (ℤ)
  • Features multiple jumps (discontinuities)
  • Non-decreasing, increasing by integers
  • No symmetry
  • Unbounded in both directions

Exponential Function

  • Formula: y = e^x
  • Domain: All real numbers
  • Range: (0, ∞)
  • No discontinuities; strictly increasing
  • No symmetry
  • Bounded below at y=0

Natural Logarithm Function

  • Formula: y = ln(x)
  • Domain: (0, ∞)
  • Range: All real numbers
  • Discontinuity at x=0 (vertical asymptote)
  • Strictly increasing
  • No symmetry
  • Unbounded in both directions

Sine Function

  • Formula: y = sin(x)
  • Domain: All real numbers
  • Range: [-1, 1]
  • Alternates between increasing and decreasing intervals
  • Displays odd symmetry around the origin
  • Bounded above at y=1 and below at y=-1

Cosine Function

  • Formula: y = cos(x)
  • Domain: All real numbers
  • Range: [-1, 1]
  • Alternates between increasing and decreasing intervals
  • Displays even symmetry across the y-axis
  • Bounded above at y=1 and below at y=-1

Logistic Function

  • Formula: y = 1/(1 + e^-x)
  • Domain: All real numbers
  • Range: (0, 1)
  • Discontinuities at y=0 and y=1 (horizontal asymptotes)
  • Strictly increasing across its domain
  • No symmetry
  • Bounded below at y=0 and above at y=1

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