Pagkakaiba ng Rational Functions at Equations

Oct 11, 2024

Pagkakaiba ng Rational Function, Rational Equation, at Rational Inequalities

Ano ang Rational Expression?

  • Rational Expression: Maaaring isulat bilang ratio ng dalawang polynomials.
    • Walang negative o fractional exponent.
    • Hindi nasa loob ng radical ang variables.
  • Halimbawa:
    • 2/x
    • (x^2 + 2x + 3)/(x + 1)
    • 5/(x - 3)

Pagsusuri ng Algebraic Expressions

  • x^2 + 3x + 2 / (x + 4): Rational expression kasi parehong polynomial ang numerator at denominator.
  • 1/(3x^2): Rational expression dahil ang numerator at denominator ay polynomial.
  • x^2 + 4x - 3 / 2: Rational expression.
  • √(x+1) / (x^3 - 1): Hindi rational expression dahil nasa loob ng radical ang numerator.
  • x^(-2) - 5 / (x^3 - 1): Hindi rational expression dahil negative ang exponent sa numerator.
  • 1/x + 2/(x-2): Rational expression kapag sinimplify.

Pagkakaiba ng Rational Equation, Inequality, at Function

Rational Equation

  • Equation na gumagamit ng rational expression.
  • Halimbawa: 5/x - 3/2x = 1/5
  • Tandaan: May symbol na "=".

Rational Inequality

  • Inequality na gumagamit ng rational expression.
  • Halimbawa: 5/x - 3 ≤ 2/x
  • Tandaan: May inequality symbols: ">", "<", "≤", "≥".

Rational Function

  • Function ng form f(x) = p(x)/q(x), kung saan ang p(x) at q(x) ay polynomial at q(x) ≠ 0.
  • Halimbawa: f(x) = (x^2 + 2x + 3)/(x + 1)
  • Tandaan: May form na f(x) o y.

Mga Practice Exercises

  1. 2 + x/(x - 1) = 8: Rational Equation
  2. x > √(x + 2): None (hindi rational)
  3. f(x) = 6 - (x + 3)/(x^2 - 5): Rational Function
  4. 2x ≥ 7/(x + 4): Rational Inequality
  5. x/2 = 4/x + 9x^3: Rational Equation

Pagsusuri:

  • Tignan kung rational ang expression.
  • Tignan ang mga simbolo para matukoy kung equation, inequality, o function.

Konklusyon

  • Rational Equation: May "=" symbol.
  • Rational Inequality: May inequality symbol (">", "<", "≤", "≥").
  • Rational Function: In form of f(x) or y.

Tandaan: Ang rational equation/inequality ay sinusolb para sa lahat ng x values na nagsasatisfy sa kondisyon, samantalang ang rational function ay nagpapakita ng relasyon sa pagitan ng dalawang variables tulad ng x at y.