Question

1. consider the adjacent graph: 7a does the function have an absolute maximum or minimum? yes, it has an absolute maximum. a no, it does not have either. b yes, it has an absolute minimum. c

Explanation:

Step1: Recall the definition of absolute maximum and minimum

An absolute maximum of a function \(y = f(x)\) on an interval is a point \((x_0,f(x_0))\) such that \(f(x_0)\geq f(x)\) for all \(x\) in the domain. An absolute minimum is a point \((x_1,f(x_1))\) such that \(f(x_1)\leq f(x)\) for all \(x\) in the domain.

Step2: Analyze the graph

Looking at the graph, as \(x\) approaches the left - hand side (since the graph is not bounded on the left, \(y\to-\infty\)) and as \(x\) approaches the right - hand side (the graph is not bounded on the right, \(y\to-\infty\)). But there is a highest point (local maximum which is also the absolute maximum) in the graph.

Answer:

A. Yes, it has an absolute maximum.