SOLUTION: let f be a function with domain (-2,positive infinity) and range [-3,4]. Find the domain and range of y=-f(x+2)-3

Algebra ->  Functions -> SOLUTION: let f be a function with domain (-2,positive infinity) and range [-3,4]. Find the domain and range of y=-f(x+2)-3       Log On


   

Question 407741: let f be a function with domain (-2,positive infinity) and range [-3,4].
Find the domain and range of y=-f(x+2)-3


Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f(x+2) corresponds to a horizontal shift of the y-axis 2 units to the right, and so the new domain is (-4, infinity).
-f(x+2)-2 implies reflection across the x-axis, and then vertical shift of x-axis 3 units up, and so the new range is [3 - 3, -4 - 3], or [0, -7].