A restriction on the domain of the graph of the quadratic function f(x) = a(x – c)^2 + d that would ensure the inverse of y = f(x) is always a function is

Question

A) x ≥ c

B) x ≥ 0

C) x ≥ d

D) x ≥ a

Answer 1

The given function has its vertex at (c, d). That means to the right of the line x = c, the parabola is increasing (or decreasing). With no restriction on c the parabola (any up/down parabola) does not pass the horizontal line test. by restricting the domain to x ≥ c, the function now passes the horizontal line test (that is the function is now 1-1), so it will have an inverse "function".

Check here so see the function and its inverse. Use the sliders on a,b,c to see different flavors:

desmos.com/calculator/pfpw2zqcjd