Question

draw a graph to match the description given
g(x) is increasing over (-\infty,5) and (9,\infty) and decreasing over (5,9)
which of the following graphs matches the description?

Explanation:

Step1: Analyze the increasing and decreasing intervals

A function \(y = G(x)\) is increasing on an interval if, as \(x\) increases, \(y\) also increases. It is decreasing if, as \(x\) increases, \(y\) decreases.

Step2: Check each graph

• For Graph A: The behavior does not match the given intervals \((-\infty,5)\) (increasing), \((5,9)\) (decreasing), \((9,\infty)\) (increasing).
• For Graph B: The function has a single - peak and does not have the three - part behavior (two increasing and one decreasing intervals as required).
• For Graph C: The function has a local minimum and does not match the given increasing - decreasing - increasing pattern.
• For Graph D:
• When \(x\in(-\infty,5)\), as \(x\) increases, \(y\) increases (function is increasing).
• When \(x\in(5,9)\), as \(x\) increases, \(y\) decreases (function is decreasing).
• When \(x\in(9,\infty)\), as \(x\) increases, \(y\) increases (function is increasing).

Answer:

D.