Question

assume arrows if no symbols are shown at the ends of the graph. state your answers using interval notation. enter dne if there is no solution. consider the function graphed below. a. the function is increasing on the interval(s): (3,5) b. the function is decreasing on the interval(s): (8,1) ∪ (5,∞) c. the function is constant on the interval(s): (-∞,8) ∪ (1,3) d. the domain of the function is: (-∞,∞) e. the range of the function is: f. the local maximum point is (5,5) g. the local minimum point is (8,-4) question help: written example submit question

Explanation:

Step1: Analyze increasing intervals

Look for parts of the graph where the y - values increase as x - values increase. We see the function is increasing from x = 3 to x = 5. So the increasing interval is $(3,5)$.

Step2: Analyze decreasing intervals

Find where y - values decrease as x - values increase. The function is decreasing for x from 5 to positive infinity and also from 8 to 1 (assuming the correct order based on the graph's shape). So the decreasing intervals are $(8,1)\cup(5,\infty)$.

Step3: Analyze constant intervals

Identify where y - values stay the same as x - values change. The function is constant from negative infinity to 8 and from 1 to 3. So the constant intervals are $(-\infty,8)\cup(1,3)$.

Step4: Determine the domain

The domain is all possible x - values. Since the graph extends infinitely in both the left - hand and right - hand directions, the domain is $(-\infty,\infty)$.

Step5: Determine the range

The range is all possible y - values. The graph extends infinitely downwards and upwards, so the range is $(-\infty,\infty)$.

Step6: Find local maximum point

The local maximum is the point where the function changes from increasing to decreasing. From the graph, this occurs at the point $(5,5)$.

Step7: Find local minimum point

The local minimum is the point where the function changes from decreasing to increasing. From the graph, this occurs at the point $(8, - 4)$.

Answer:

a. $(3,5)$
b. $(8,1)\cup(5,\infty)$
c. $(-\infty,8)\cup(1,3)$
d. $(-\infty,\infty)$
e. $(-\infty,\infty)$
f. $(5,5)$
g. $(8,-4)$