Maximum and minimum values, power functions

Ukrainian Grade 10 (algebra and calculus, §1, sections 1 to 3): greatest and least values, power functions with a natural exponent and with an integer exponent.

f(x₀) is the greatest value of f on a set M if x₀ ∈ M and f(x) ≤ f(x₀) for every x ∈ M. It is written maxf(x) = f(x₀), x ∈ M; the least value is min. A function may have no greatest or no least value on a set.

For y = xⁿ, n a natural number: for even n the function is even, decreasing on (−∞, 0] and increasing on [0, ∞); for odd n it is odd and increasing on ℝ.

y = x⁻ⁿ is defined for x ≠ 0. For even n it is even with range (0, ∞); for odd n it is odd with range (−∞, 0) ∪ (0, ∞).