Question

use the graph below to determine whether the function is increasing, decreasing, constant, or undefined over the given interval.

question 6 (3 points)
interval: $(-\infty, -3)$
\\(\circ\\) a increasing
\\(\circ\\) b decreasing
\\(\circ\\) c constant
\\(\circ\\) d undefined

Explanation:

Step1: Recall function behavior definitions

A function is increasing on an interval if, as \( x \) increases, \( y \) (the function's value) also increases. A function is decreasing if \( y \) decreases as \( x \) increases, constant if \( y \) stays the same, and undefined if there's no corresponding \( y \) for \( x \) in the interval.

Step2: Analyze the graph on \((-\infty, -3)\)

For the interval \((-\infty, -3)\), observe the graph. As \( x \) values increase (moving from left to right towards \( -3 \)), the \( y \)-values of the function are also increasing (the line is going up from left to right in this interval).

Answer:

a. Increasing