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

A graph of a function f is given. (a) Find f(-2) and f(2). (b) Find the net change and the average rate of change of f between x =-2 and x = 2. (c) Find the domain and range of f. (d) On what intervals is f increasing? On what intervals is f decreasing? (e) What are the local maximum values of f? (f) Is f one-to-one?

Solution

Ans(a):
f(-2) means find y-value when x=-2 so answer is
f(-2)=-1
similarly
f(2)=2
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Ans(b):
Net change of f between x=-2 and 2 is given by
f(2)-f(-2)=2-(-1)=3

Average rate of change is given by
[f(b)-f(a)]/[b-a]
=[f(2)-f(-2)]/[2-(-2)]
=[3]/[4]
=3/4
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Ans(c):
domain includes set of x-points that is covered by graph
so domain = [-4,5]
range includes set of y-points that is covered by graph
so range = [-4,4]
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Ans(d):
Interval in which slope of graph is positive is called interval of increasing.
so increasing intervals are: (-4,-2), (-1,4)
just opposite for decreasing
so decreasing intervals are: (-2,-1), (4,5)
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Ans(e):
Horizontal line test is used to check for one to one.
If you draw any horizontal line between 3 and 4 on y-axis then that line will cross the graph at more than one point.
Hence it is NOT one to one.