use the graph to determine\n(a) open intervals on which the\nfunction is increasing, if any\n(b) open…
use the graph to determine\n(a) open intervals on which the\nfunction is increasing, if any\n(b) open intervals on which the\nfunction is decreasing, if any\n(c) open intervals on which the\nfunction is constant, if any.\n\n(a) 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) (0,4)\n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. the function is never increasing\n\n(b) select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the function is decreasing on the interval(s)\n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. the function is never decreasing.
Answer
Explanation:
Step1: Recall the definition of increasing function
A function (y = f(x)) is increasing on an open 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)). From the graph, we can see that as (x) moves from (0) to (4), the (y -)value of the function is rising. So the function is increasing on ((0,4)).
Step2: Recall the definition of decreasing function
A function (y = f(x)) is decreasing on an open 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)). Looking at the graph, there is no interval where the (y -)value of the function is falling as (x) increases.
Step3: Recall the definition of constant function
A function (y = f(x)) is constant on an open 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)). There is no interval where the (y -)value of the function remains the same as (x) increases.
Answer:
(a) A. The function is increasing on the interval(s) ((0,4)) (b) B. The function is never decreasing (c) The function is never constant.