Increasing and Decreasing Functions, Piecewise Functions II. Consider the function f(x). Identify the domain and range of f(x), draw its graph and label points if necessary, and determine whether or not f(x) is monotonic on the following intervals. If f(x) is monotonic on an interval, specify whether increasing or decreasing (no constant). Domain and Range of f(x); Graph of f(x): f(x) = -(x-11)²+5 2²/12 |3x=15-3 6x-6 -x-2 3x + 12 -(x + 5)²-1 -(x + 10)²+5 x + 15 if x > 10 if 8 < x < 10 if 3 < x < 8 if 0 < x < 3 if -4 < x < 0 if -7
Increasing and Decreasing Functions, Piecewise Functions II. Consider the function f(x). Identify the domain and range of f(x), draw its graph and label points if necessary, and determine whether or not f(x) is monotonic on the following intervals. If f(x) is monotonic on an interval, specify whether increasing or decreasing (no constant). Domain and Range of f(x); Graph of f(x): f(x) = -(x-11)²+5 2²/12 |3x=15-3 6x-6 -x-2 3x + 12 -(x + 5)²-1 -(x + 10)²+5 x + 15 if x > 10 if 8 < x < 10 if 3 < x < 8 if 0 < x < 3 if -4 < x < 0 if -7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Increasing and Decreasing Functions, Piecewise Functions
II. Consider the function f(x). Identify the domain and range of f(x), draw its graph and label
points if necessary, and determine whether or not f(x) is monotonic on the following intervals.
If f(x) is monotonic on an interval, specify whether increasing or decreasing (no constant).
Domain and Range of f(x); Graph of f(x):
1. (-∞, - 10)
2. (-10,-7)
f(x) =
3. (-7,-4)
4. (-4,0)
5. (0,3)
-(x-11)²+5 if x > 10
3x - 15
2
-
-=-
6. (3,8)
7. (8,10)
8. (10, +∞0)
9. (-∞, -8)
10. (-7,-5)
3
6x-6
-x-2
3x + 12
-(x + 5)²-1
-(x + 10)²+5
x + 15
Hint: Draw the graph of f(x) on the coordinate plane where x € (-15,15) and y € (-10,10).
If necessary, you may just draw arrows to indicate that the graph of f(x) continues beyond
these boundaries.
if 8 < x < 10
if 3 < x < 8
if 0 < x < 3
if -4 < x < 0
if -7<x< - 4
if -10 < x < -7
if x < -10
11. (-5,0)
12. (-5,1)
13. (0,1)
14.
(1,2)
15. (2,5)
16. (4,5)
17. (5,10)
18. (8,10)
19. (6,11)
20. (11, +∞0)
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