use the graph to determine (a) intervals on which the function is increasing, if any. (b) intervals on which…
use the graph to determine (a) intervals on which the function is increasing, if any. (b) intervals on which the function is decreasing, if any. (c) intervals on which the function is constant, if any. (a) use the graph to determine intervals on which the function is increasing, if any. select the correct choice below a. the function is increasing on the interval(s) (-∞, -3), (-3, -2) (type your answer in interval notation. use a comma to separate answers as needed.)
Answer
Explanation:
Step1: Recall increasing - function definition
A function is increasing when as (x) increases, (y) also increases.
Step2: Analyze the graph
Looking at the given graph, we see that the function goes up as (x) moves from (-\infty) to (- 3) and then from (-3) to (-2).
Step3: Write in interval notation
The intervals are ((-\infty,-3)) and ((-3,-2)).
Step4: Recall decreasing - function definition
A function is decreasing when as (x) increases, (y) decreases.
Step5: Analyze the graph for decreasing part
The function is decreasing on the intervals ((-2, - 1)) and ((-1,\infty)).
Step6: Recall constant - function definition
A function is constant when (y) does not change as (x) changes.
Step7: Analyze the graph for constant part
There are no intervals where the function is constant.
Answer:
(a) The function is increasing on the interval(s) ((-\infty,-3),(-3,-2)) (b) The function is decreasing on the interval(s) ((-2,-1),(-1,\infty)) (c) There are no intervals on which the function is constant.