College Algebra

Graph the function using transformations. Show your work and state
a) the domain
b) the range
c) the asymptotes
f(x) = 3 - 1/(x + 4)^2

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  1. if g(x) = 1/x^2

    1/(x+4)^2 is g(x) shifted left 4 units
    -1/(x+4)^2 flips it over the y-ais
    3 - 1/(x+4)^2 shifts it up 3 units

    so, f(x) is 1/x^2 shifted left, reflected, and then shifted up.

    Same with the asymptotes, which I am sure you can figure out for 1/x^2.

    domain is all reals except x = -4
    range is all reals < 3

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