Question

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

1. (5, ∞)
2. (-∞, 5)
3. (5, 8)
4. (2, 5)

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

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. \((5,\infty)\)