A graph of a function f is given Find f2 and f2 Find the dom

A graph of a function f is given, Find f(-2) and f(2) Find the domain and range of f. On what intervals if f Increasing? On what intervals is f decreasing? What are the local maximum values of f? If f one-to-one?

Solution

a)
f(-2)=-1
f(2)=2
b)
All the values on x axis are domain.
So domain is [-4,5], both end points are inclusive.
c)
Slope of the tangent is positive then f is increasing and slope of the tangent is negative then function is decreasing.
So increasing (-4,-1.5) U (-0.5, 4)
Decreasing (-1.5, -0.5) U (4,5)
d) Point where, slope of derivative is changing from positive to negative, then f has local maxima.
=> x=-1.5 and x=4 are local maxima.