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Function Operations quiz

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  • How do you add two functions, such as f(x) = x^2 + 4 and g(x) = 5x + 7?
    You add the corresponding terms to get x^2 + 5x + 11.
  • What is the domain of the sum or difference of two functions?
    It is the intersection of the domains of the individual functions, considering any restrictions like division by zero.
  • What restriction must you consider when a function has a denominator of x?
    x cannot be equal to 0 because division by zero is undefined.
  • How do you subtract h(x) = x + sqrt(x-8) from g(x) = x^2 + x + 2?
    You distribute the negative sign and combine like terms to get x^2 + 2 - sqrt(x-8).
  • What is the domain of h(x) = x + sqrt(x-8)?
    x must be greater than or equal to 8 because the expression under the square root cannot be negative.
  • When multiplying f(x) = sqrt(x) and g(x) = 3x - 6, what is the resulting function?
    The result is 3x*sqrt(x) - 6*sqrt(x).
  • What is the domain of f(x) = sqrt(x)?
    The domain is all real numbers x such that x ≥ 0.
  • What additional restriction must you consider when dividing functions?
    The denominator cannot be zero, so any x that makes the denominator zero must be excluded from the domain.
  • If f(x) = sqrt(x) and g(x) = 3x - 6, what is the domain of f(x)/g(x)?
    The domain is x ≥ 0 and x ≠ 2, since 3x - 6 = 0 when x = 2.
  • How do you multiply f(x) = x^2 - 4 and g(x) = x + 2?
    Use the distributive property (FOIL) to get x^3 + 2x^2 - 4x - 8.
  • What is the domain of the product of two polynomials?
    The domain is all real numbers, since polynomials are defined everywhere.
  • How do you divide f(x) = x^2 - 4 by g(x) = x + 2 and simplify?
    Factor the numerator to (x + 2)(x - 2), cancel x + 2, and get x - 2, but x ≠ -2.
  • Why must you find domain restrictions before simplifying a division of functions?
    Because simplification can remove factors that cause restrictions, but the original domain restrictions still apply.
  • What does the notation (f + g)(x) mean?
    It means f(x) + g(x), the sum of the two functions evaluated at x.
  • What does the notation (f/g)(x) mean?
    It means f(x) divided by g(x), with the domain restricted so that g(x) ≠ 0.