use the graph of the function f given below to answer the question. is f increasing on the interval -5,0…
use the graph of the function f given below to answer the question. is f increasing on the interval -5,0? yes no
Answer
Explanation:
Step1: Recall the definition of an increasing function
A function (y = f(x)) is increasing on an interval ([a,b]) if for any (x_1,x_2\in[a,b]) with (x_1<x_2), we have (f(x_1)<f(x_2)). Graphically, the function rises as (x) moves from left - to - right on the interval.
Step2: Analyze the graph on the interval ([-5,0])
On the interval ([-5,-2]), the function is increasing (as (x) increases from (-5) to (-2), (y) increases from (0) to (9)). But on the interval ([-2,0]), as (x) increases from (-2) to (0), (y) decreases from (9) to (5). Since the function does not satisfy the condition of being increasing for all sub - intervals of ([-5,0]) (it has a decreasing part on ([-2,0])), the function (f) is not increasing on the entire interval ([-5,0]).
Answer:
No