III. Suppose that a function f(x) satisfies the following properties, together with the table of signs given below. • dom f = R\{-1} lim f(x) = 2 lim_ f(x) = +∞ I→-1+ lim [f(x)(1-x)] = 0 lim f(x) =18 8118 2--1- +1 (-1,0) 0 2 (2, +∞) f und 0 1 f' und 0 + + + f" und + + + 0 1. Identify the equations of all the linear asymptotes of f. 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave up/down. 3. Identify the relative maximum points, relative minimum points and points of inflection of f, if any. 4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equa- tions and label all relative extremum point/s and point/s of inflection with their coordinates. (-∞, -1) ∞++x (0,2)
III. Suppose that a function f(x) satisfies the following properties, together with the table of signs given below. • dom f = R\{-1} lim f(x) = 2 lim_ f(x) = +∞ I→-1+ lim [f(x)(1-x)] = 0 lim f(x) =18 8118 2--1- +1 (-1,0) 0 2 (2, +∞) f und 0 1 f' und 0 + + + f" und + + + 0 1. Identify the equations of all the linear asymptotes of f. 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave up/down. 3. Identify the relative maximum points, relative minimum points and points of inflection of f, if any. 4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equa- tions and label all relative extremum point/s and point/s of inflection with their coordinates. (-∞, -1) ∞++x (0,2)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
Related questions
Question
![III. Suppose that a function f(x) satisfies the following properties, together with the table of signs
given below.
• dom f = R\{-1}
lim f(x) = 2
●
lim_ f(x) = +∞
x-1+
lim [f(x) (1 x)] = 0
lim f(x) ==∞
I-X
H--1-
+1 (-1,0) 0
2
(2, +∞)
f
und
0
1
f'
und
0
+ +
+
f"
und
+
+ +
0
1. Identify the equations of all the linear asymptotes of f.
2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave
up/down.
3. Identify the relatíve maximum points, relative minimum points and points of inflection of f,
if any.
4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equa-
tions and label all relative extremum point/s and point/s of inflection with their coordinates.
-∞, -1)
●
8+←1
(0, 2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a50c14d-2772-4b08-bf04-7f2c201c67f9%2Fabad975c-2d27-4cd8-824e-67398b389734%2Fvk2pyxwb_processed.png&w=3840&q=75)
Transcribed Image Text:III. Suppose that a function f(x) satisfies the following properties, together with the table of signs
given below.
• dom f = R\{-1}
lim f(x) = 2
●
lim_ f(x) = +∞
x-1+
lim [f(x) (1 x)] = 0
lim f(x) ==∞
I-X
H--1-
+1 (-1,0) 0
2
(2, +∞)
f
und
0
1
f'
und
0
+ +
+
f"
und
+
+ +
0
1. Identify the equations of all the linear asymptotes of f.
2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave
up/down.
3. Identify the relatíve maximum points, relative minimum points and points of inflection of f,
if any.
4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equa-
tions and label all relative extremum point/s and point/s of inflection with their coordinates.
-∞, -1)
●
8+←1
(0, 2)
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