Let f be the function with the graph below Find the domain o

Let f be the function with the graph below. Find the domain of f. Find the range of f. Find the intervals on which f is increasing. Find the intervals on which f is decreasing. Find the intervals on which f is constant. Find the absolute in ax i mu ins of f. Find the absolute minimums of f. Find the relative maximums of f. Find the relative minimums of f.

Solution

a) domain is all values of x where graph exists

from the graph we can see that graph exists from x = -3 to x =4 the x = 5 to x=9

so domain is [-3 , 4 ] U [ 5 ,9 ]

b) range is all values of y where graph exists

from the graph we can see that graph exists from y = 8 to y = 2 then y =1 to y = -1

therefore, range is (-1 , 1] U [ 2 , 8 ]

c) f increasing means interval at which function is increasing that is goung up

[-3,-2) U (2,4]

d) f decreasing means interval at which function is decreasing that is going down

(-2,2) U [5,7)

e) f is constant at [ 7,9 ]

f) absolute maximum is at (-2,8)

g) absolute minimum is at (2,2)