use the graph to determine\na. open intervals on which the function is increasing, if any.\nb. open…
use the graph to determine\na. open intervals on which the function is increasing, if any.\nb. open intervals on which the function is decreasing, if any.\nc. open intervals on which the function is constant, if any.\na. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the function is increasing on the interval(s) (0,∞). (type your answer in interval notation. use a comma to separate answers as needed.)\nb. there is no interval on which the function is increasing
Answer
Explanation:
Step1: Analyze the graph's slope
A function is increasing when its slope is positive. Looking at the graph, as we move from left - to - right, the function rises from $x = - 2$ to $x=2$.
Step2: Write the increasing interval
The open interval where the function is increasing is $(-2,2)$.
Step3: Analyze decreasing intervals
A function is decreasing when its slope is negative. The function falls for $x<-2$ and $x > 2$. The open intervals of decrease are $(-\infty,-2)$ and $(2,\infty)$.
Step4: Analyze constant intervals
The function is not flat (has non - zero slope everywhere on the visible part of the graph), so there are no intervals where it is constant.
Answer:
a. The function is increasing on the interval(s) $(-2,2)$ b. The function is decreasing on the interval(s) $(-\infty,-2),(2,\infty)$ c. There is no interval on which the function is constant.