Natural Logarithms Domain and Range

• logarithmic parent function

• natural logarithm function

• natural base exponential function

Let f(x) = ln x. Identify the minimum and maximum values over the specified interval, or state that a maximum or minimum does not exist. [1, 5]

• all real numbers

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Find the Domain and Range

• Domain: (-∞, ∞)

  Range: ( -2, ∞)

• Domain: (-∞, ∞)

  Range: ( -∞, -2)

• Domain: ( -∞, -2)

  Range: (-∞, ∞)

• Domain: ( -2, ∞)

  Range: (-∞, ∞)

Describe the domain and range of a basic logarithmic function.

• Domain: All real numbers, Range: All real numbers

• Domain: All positive real numbers, Range: All real numbers

• Domain: All negative real numbers, Range: All real numbers

• Domain: All real numbers, Range: All positive real numbers

Explain the domain and range of the parent function graph of a logarithmic function.

• Domain: x > 0, Range: y ∈ R

• Domain: x ∈ R, Range: y > 0

• Domain: x > 0, Range: y > 0

• Domain: x < 0, Range: y ∈ R

Find the Domain and Range

• Domain: (-∞, ∞)

  Range: ( -2, ∞)

• Domain: (-∞, ∞)

  Range: ( -∞, -2)

• Domain: ( -∞, -2)

  Range: (-∞, ∞)

• Domain: ( -2, ∞)

  Range: (-∞, ∞)

Graph

• A

• B

• C

• D

ln(2) = x

• 2^x = 10

• 10² = x

• e^x = 2

• e² = x