Gen Math

• INEQUALITY


  Rational<|>Exponential<|>Logarithmic
• INEQUALITY


  • 25 < log5 x
  • 5x + 2 > 3x5
  • 2x ≤ xx
  • 4 ≥ 2x
• EQUATION


  Rational<|>Exponential<|>Logarithmic
• FUNCTION


  Rational<|>Exponential<|>Logarithmic
• REAL-LIFE APPLICATION


  Exponential<|>Logarithmic<|>One-to-one<|>Piecewise<|>Rational
• REAL-LIFE APPLICATION


  • Bacteria doubling every minute
  • Jeepney fare vs distance
  • Student ID to learner reference number
  • Carbon dating
  • Manpower needed vs time
• 3x = 32
• log2 x = log2 16
• 0.5x < 0.53
• log0.3 x > 2
• 9/x = 3
• 1/x ≤ 0
• Domain


  The set of non-negative real numbers<|>The set of non-zero real numbers<|>The set of positive real numbers<|>The set of all real numbers
• Domain of f(x) = 5^x


  • The set of all real numbers
• Range of f(x) = 5^x


  • The set of positive real numbers
• Domain of g(x) = log5 x

  • The set of positive real numbers
• Range of g(x) = log5 x

  • The set of all real numbers
• Domain of h(x) = 5/x^3


  • The set of non-zero real numbers
• Range of h(x) = 5/x^3


  • The set of non-zero real numbers
• Range of k^-1(x)


  • The set of non-negative real numbers
• Domain of k^-1(x)


  • The set of all real numbers
• Inverse of the function whose graph is shown
• Number of zeros


  None<|>Only 1<|>At most 1<|>At least 1
• Number of zeros of the logarithmic function in 9A


  • None
• Number of zeros of the exponential function in 9B


  • None
• Number of zeros of the exponential function in 9C

  • None
• Number of zeros of the exponential function in 9D

  • Only 1
• Number of y-intercepts


  None<|>Only 1<|>At most 1<|>At least 1
• Number of y-intercepts of a rational function

  • At most 1
• Number of y-intercepts of an exponential function f(x) = b^x


  • Only 1
• Number of y-intercepts of a logarithmic function f(x) = log_b x


  • Only 1
• f(x) = ((x-a)(x-b)(x-c)(x-d))/(x-p)(x-q)(x-r))
• f(x)


  • x, x < 0

  x, x ≥ 0
• f(p) = 5 and g(p) = -4


  f + g gives the greatest value

  f - g gives the least value
• Inverse of f(x) = x + 5

  f^-1(x) = x - 5
• To find the inverse of f


  Use (f + g)(x) = 0, (f/h)(x) = 1, (fk)(x) = x^2, and (f ∘ m)(x) = x
• To find f(x) when (f ∘ g)(x) = 5x and g(x) = 3 - x

  f(x) = 15 - 5x
• To solve for p(x) when (p ∘ q)(x) and q(x) are known


  Use (p ∘ q)[q^-1(x)]
• The half life of a chemical is 6 hours. The feeds were graded to be safe for chicken consumption with not more than 12.5% contamination of that chemical.
• Function illustrated by the table

  f(x) = log4 x