Question

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

Answer 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