a. open intervals on which the function is increasing, if any. b. open intervals on which the function is…
a. open intervals on which the function is increasing, if any. b. open intervals on which the function is decreasing, if any. c. open intervals on which the function is constant, if any. the function is decreasing on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. there is no interval on which the function is decreasing. c. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function is constant on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed.) b. there is no interval on which the function is constant.
Answer
Explanation:
Step1: Recall increasing - function concept
A function is increasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, then $f(x_1)<f(x_2)$. Looking at the graph, the function is increasing on the intervals $(-\infty, - 1)$ and $(1,\infty)$.
Step2: Recall decreasing - function concept
A function is decreasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, then $f(x_1)>f(x_2)$. The function is decreasing on the interval $(-1,1)$.
Step3: Recall constant - function concept
A function is constant on an interval if for any two points $x_1$ and $x_2$ in the interval, $f(x_1)=f(x_2)$. From the graph, there is no such interval.
Answer:
a. $(-\infty, - 1),(1,\infty)$ b. $(-1,1)$ c. B. There is no interval on which the function is constant.