Question

Find the range of the given function f(x)=(x-1)^2+1

Answer 1

Answer:

  a.)  [1, infinity)

Step-by-step explanation:

The equation is that of a parabola that opens upward with vertex (1, 1). Hence the minimum value of f(x) is 1, and all values greater than that are part of the range: [1, ∞).

_____

The "vertex form" of the equation of a parabola is ...

  f(x) = a(x -h)^2 + k

The vertex is at (h, k). When a > 0, the parabola opens upward. When a < 0, the parabola opens downward. Whichever way it opens, the value k is an extreme value and the limit of the range.