Question

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

a.) [1, infinity)
b.) (- infinity, infinity)
c.) [0, infinity)
d.) (- infinity, 1)

Answer 1

a.) [1, infinity)

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, ∞).

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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.