Question

complete the sentence below.
a f
on f is — on an interval i if, for any choice of x₁ and x₂ in i, with x₁ < x₂, we have f(x₁) < f(x₂).
a function f is — on an interval i if, for any choice of x₁ and x₂ in i, with x₁ < x₂, we have f(x₁) < f(x₂).
constant
decreasing
increasing

Explanation:

A function \( f \) is called increasing on an interval \( I \) when for any two points \( x_1,x_2\in I \) with \( x_1 < x_2 \), the inequality \( f(x_1)<f(x_2) \) holds. A constant function has \( f(x_1)=f(x_2) \) for all \( x_1,x_2\in I \), and a decreasing function has \( f(x_1)>f(x_2) \) when \( x_1 < x_2 \).

Answer:

increasing