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(j) List the intervals where f is decreasing.
(k) List the local maximums, if any exist.
(l) List the local minimums, if any exist.
(m) Find the maximum, if it exists.
(n) Find the minimum, if it exists.
(o) Is f even, odd, or neither? 78 Relations and Functions
4. Use your graphing calculator to approximate the local and absolute extrema of the following
functions. Approximate the intervals on which the function is increasing and those on which
it is decreasing. Round your answers to two decimal places.
(a) f (x) = x4 − 3x3 − 24x2 + 28x + 48
(c) f (x) = 9 − x2
(b) f (x) = x2/3 (x − 4)
(d) f (x) = x 9 − x2
5. Sketch the graphs of the following piecewise-deﬁned functions. x2 if x ≤ −2
−2x − 4 if x < 0 (a) f (x) =
(c) f (x) =
3 − x if −2 < x < 2
3x if x ≥ 0 4 if x ≥ 2 1 if −6 < x < −1 x
(d) f (x) =
x + 4 if −4 ≤ x < 5 √x if −1 < x < 1
(b) f (x) =
√ x − 1 if x ≥ 5
x if 1 < x < 9
6. Let f (x) = x , the greatest integer function deﬁned in Exercise 12 in Section 1.5.
(a) Graph y = f (x). Be careful to correctly describe the behavior of the graph near the...
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