from the graph of the function, state the domain, the range, and the intervals on which the function is…

from the graph of the function, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant. complete parts (a) and (b). (a) the domain is $(-\\infty,\\infty)$. (type your answer in interval notation.) the range is $(-\\infty,0$. (type your answer in interval notation.) on what interval(s) is the function increasing? select the correct choice below and, if necessary, fill in the answer a. the function is increasing on $(-\\infty,0$. (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never increasing. on what interval(s) is the function decreasing? select the correct choice below and, if necessary, fill in the answer a. the function is decreasing on $0,\\infty)$. (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never decreasing. on what interval(s) is the function constant? select the correct choice below and, if necessary, fill in the answer a. the function is constant on (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never constant.

from the graph of the function, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant. complete parts (a) and (b). (a) the domain is $(-\\infty,\\infty)$. (type your answer in interval notation.) the range is $(-\\infty,0$. (type your answer in interval notation.) on what interval(s) is the function increasing? select the correct choice below and, if necessary, fill in the answer a. the function is increasing on $(-\\infty,0$. (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never increasing. on what interval(s) is the function decreasing? select the correct choice below and, if necessary, fill in the answer a. the function is decreasing on $0,\\infty)$. (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never decreasing. on what interval(s) is the function constant? select the correct choice below and, if necessary, fill in the answer a. the function is constant on (type your answer in interval notation. use a comma to separate answers as needed.) b. the function is never constant.

Answer

Explanation:

Step1: Analyze the function's increasing interval

For a function, if as (x) increases, (y) also increases, the function is increasing. Looking at the graph, from (-\infty) to (0), as (x) values get larger (moving from left to right), the (y) - values of the function are getting larger. So the function is increasing on ((-\infty,0]).

Step2: Analyze the function's decreasing interval

For a function, if as (x) increases, (y) decreases, the function is decreasing. Looking at the graph, from (0) to (\infty), as (x) values get larger (moving from left to right), the (y) - values of the function are getting smaller. So the function is decreasing on ([0,\infty)).

Step3: Analyze the function's constant interval

For a function to be constant, as (x) increases, (y) remains the same. Looking at the graph, there is no interval where the (y) - value of the function does not change as (x) changes.

Answer:

  • For the increasing interval: A. The function is increasing on ((-\infty,0])
  • For the decreasing interval: A. The function is decreasing on ([0,\infty))
  • For the constant interval: B. The function is never constant.