draw a graph to match the description given\ng(x) is increasing over (-\\infty,5) and (9,\\infty) and…
draw a graph to match the description given\ng(x) is increasing over (-\\infty,5) and (9,\\infty) and decreasing over (5,9)\nwhich of the following graphs matches the description?
Answer
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.