Click for List local minimum local maximum inflection point vertical asymptote other We wish to sketch the graph of the function 22-112+28 f(x) = (x - 5)2 • Find all the critical numbers of f and of f' (that is, all potential extrema and/or inflection points). There are two of them; enter their exact values, together with the value = 5 at which f is undefined, in the first column of the table below (in ascending order: a < b < c). The second column consists of several drop-down menus. Analyse the graph off and then do the following: . for each of the intervals defined by these points, select the phrase that best describes the behaviour and shape of the graph of the function f; • for each of the critical numbers, select the phrase that best describes their nature; • for each of too and x = 5, select the phrase that best describes the corresponding limiting behaviour of f. behavior -∞ horizontal asymptote x c Click for List horizontal asymptote Click for List increasing, concave downward increasing, concave upward decreasing, concave downward decreasing, concave upward

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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nghngi
We wish to sketch the graph of the function
11x + 28
f(x) :
(x – 5)2
• Find all the critical numbers of f and of f' (that is, all potential extrema and/or inflection points). There are two of them;
enter their exact values, together with the value x = 5 at which f is undefined, in the first column of the table below (in
ascending order : a < b < c).
The second column consists of several drop-down menus. Analyse the graph of f and then do the following:
• for each of the intervals defined by these points, select the phrase that best describes the behaviour and shape of the
graph of the function f;
• for each of the critical numbers, select the phrase that best describes their nature;
for each of ±0o and x =
5, select the phrase that best describes the corresponding limiting behaviour of f.
behavior
horizontal asymptote
Click for List
x < a
Click for List
increasing, concave downward
Click for List
固助
Click for List
a =
increasing, concave upward
local minimum
decreasing, concave downward
a < x < b
Click for List
local maximum
decreasing, concave upward
inf
ction point
b =
Click for List
vertical asymptote
b < x < c
Click for List
other
с —
Click for List
x > c
Click for List
horizontal asymptote
Transcribed Image Text:nghngi We wish to sketch the graph of the function 11x + 28 f(x) : (x – 5)2 • Find all the critical numbers of f and of f' (that is, all potential extrema and/or inflection points). There are two of them; enter their exact values, together with the value x = 5 at which f is undefined, in the first column of the table below (in ascending order : a < b < c). The second column consists of several drop-down menus. Analyse the graph of f and then do the following: • for each of the intervals defined by these points, select the phrase that best describes the behaviour and shape of the graph of the function f; • for each of the critical numbers, select the phrase that best describes their nature; for each of ±0o and x = 5, select the phrase that best describes the corresponding limiting behaviour of f. behavior horizontal asymptote Click for List x < a Click for List increasing, concave downward Click for List 固助 Click for List a = increasing, concave upward local minimum decreasing, concave downward a < x < b Click for List local maximum decreasing, concave upward inf ction point b = Click for List vertical asymptote b < x < c Click for List other с — Click for List x > c Click for List horizontal asymptote
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