Exercise 6.2.1: composition of relations expressed as a set of pairs. about here are two relations defined on the set {a, b, c, d}: s = { (a, b), (a, c), (c, d), (c, a) } r = { (b, c), (c, b), (a, d), (d, b) } write each relation as a set of ordered pairs.

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step-by-step explanati∵∵∴∴on:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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