Example 8. The graph of the function f is given below. (a) Find the intervals on

Question

Example 8. The graph of the function f is given below. (a) Find the intervals on which the function is increasing or decreasing (b) Find the domain and the range of f. (-3, 2.25) (-2.75, 0) 1.5,0.14) 1,-0.42) 2 -2.667) 3 .2 (c) Find the value(s) of a at which f has a local mi. What are the local minimum values? d) Find the value(s) of at which f has a local maximum. What are the local (e) Find the absolutely minimum and absolutely maximum, if they exist. (f) Find the value(s) of a, such that (x)0. maximum values

Explanation / Answer

a. The graph goes up or increasing in the interval (-2,0)U(1,1.5) and goes down in the interval (-3,-2)U(0,1)

b. Domain

x values are from -3 to 1.5. SO domain is [-3,1.5]

Range

y values are from -2 to 2.So range [-2,2]

c.Local minimum is at x=1 which is -0.42

d. local maximum is at x=0 which is 0 .

e.absolute minimum is at x=-2 which is -2.667 .

f. f(x)=0

It means value of x when y=0 which are x=-2.75 and x=0

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