1. (02.01)

The figure shows triangle PQR and some of its transformed images on a coordinate grid:

A coordinate plane is shown with five triangles. Triangle PQR has vertices 2 comma 1, 5 comma 1, and 2 comma 4. Triangle A has vertices negative 2 comma 1, negative 5 comma 1, and negative 5 comma 4. Triangle B has vertices negative 6 comma 1, negative 6 comma 4, and negative 9 comma 1. Triangle C has vertices negative 2 comma negative 1, negative 2 comma negative 4, negative 5 comma negative 4. Triangle D has vertices 2 comma negative 1, 5 comma negative 1, and 5 comma negative 4.
Which of the four triangles was formed by a translation of triangle PQR? (4 points)

A
B
C
D

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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