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Function Operations quiz

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  • How do you add two functions f(x) and g(x)?
    You add two functions by combining like terms, just as you would with polynomials.
  • What is the domain of the sum of two functions?
    The domain of the sum is the intersection of the domains of the individual functions.
  • What restriction Hudson applies to the domain when a function has a variable in the denominator?
    The domain excludes any value that makes the denominator zero.
  • How do you subtract one function from another?
    You subtract by distributing the negative sign and then combining like terms.
  • What domain restriction is introduced by a square root in a function?
    The expression inside the square root must be non-negative, so the domain is restricted to values making the radicand greater than or equal to zero.
  • How do you multiply two functions f(x) and g(x)?
    You multiply the functions by distributing terms, similar to multiplying polynomials.
  • What is the domain of the product of two functions?
    The domain is the intersection of the domains of the individual functions.
  • How do you divide one function by another?
    You divide by writing one function as the numerator and the other as the denominator, ensuring the denominator is not zero.
  • What additional domain restriction is introduced when dividing functions?
    The denominator cannot be zero, so any value making the denominator zero is excluded from the domain.
  • What does the notation f+g(x) mean?
    It means f(x) plus g(x), or the sum of the two functions.
  • How do you find the domain of f(x) = x squared plus 1 over x?
    The domain is all real numbers except x = 0, since division by zero is undefined.
  • If h(x) = x + sqrt(x-8), what is the domain of h?
    The domain is x ≥ 8, because the expression inside the square root must be non-negative.
  • What is the simplified form of (x squared minus 4) divided by (x plus 2)?
    It simplifies to x - 2, but the domain excludes x = -2 due to the original denominator.
  • When multiplying f(x) = sqrt(x) and g(x) = 3x - 6, what is the domain of the product?
    The domain is x ≥ 0, since sqrt(x) is only defined for non-negative x.
  • Why should you determine the domain restrictions before simplifying a function operation?
    Because simplification can hide original restrictions, so you must consider the domains before canceling terms.