Question

1. describe the end - behavior of the function graphed below.

(a) as (x\to-infty,f(x)\to-infty); as (x\to+infty,f(x)\to+infty)
(b) as (x\to-infty,f(x)\to-infty); as (x\to+infty,f(x)\to-infty)
(c) as (x\to-infty,f(x)\to+infty); as (x\to+infty,f(x)\to-infty)
(d) as (x\to-infty,f(x)\to+infty); as (x\to+infty,f(x)\to+infty)

Explanation:

Step1: Analyze left - hand end behavior

As \(x\) approaches negative infinity (\(x\to-\infty\)), looking at the left - hand side of the graph, the \(y\) - values (i.e., \(f(x)\)) are increasing. So \(f(x)\to+\infty\).

Step2: Analyze right - hand end behavior

As \(x\) approaches positive infinity (\(x\to+\infty\)), looking at the right - hand side of the graph, the \(y\) - values (i.e., \(f(x)\)) are increasing. So \(f(x)\to+\infty\).

Answer:

A. As \(x\to-\infty,f(x)\to+\infty\); as \(x\to+\infty,f(x)\to+\infty\)