the graph of f(x) is shown below. which of the following describes the interval on which the graph of f(x)…

the graph of f(x) is shown below. which of the following describes the interval on which the graph of f(x) is decreasing?\n1. (5, ∞)\n2. (-∞, 5)\n3. (5, 8)\n4. (2, 5)

the graph of f(x) is shown below. which of the following describes the interval on which the graph of f(x) is decreasing?\n1. (5, ∞)\n2. (-∞, 5)\n3. (5, 8)\n4. (2, 5)

Answer

Explanation:

Step1: Recall the definition of a decreasing function

A function (y = f(x)) is decreasing on an interval if, for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)>f(x_2)). Graphically, this means that as (x) increases, the (y -)value of the function decreases.

Step2: Analyze the given graph

The vertex of the parabola (which is a maximum point for this downward - opening parabola) is at (x = 5). For (x>5), as (x) increases (moves to the right on the (x -)axis), the (y -)value of the function (y = f(x)) decreases.

Answer:

  1. ((5,\infty))