In this question, we'll gather information for sketching the function 1. For which values of a is f(x) continuous? f(x) is continuous for a in the interval 2. Where does this function cross the x-axis? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. x = 3. Where does this function cross the y-axis? f(0) = 4. Does f(x) have any horizontal asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Horizontal asymptote(s) at y = 5. Does f(x) have any vertical asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Vertical asymptote(s) at x = 6. For large positive values of x, which function below is f(x) asymptotic to? For large positive x, f(x) = ○1 ○ ea ○ log(2) Ox 7. Find the first and second derivatives of f(x). f'(x) = f" (x) = # 8. Give all values of x for which f'(x) exists and is negative. If there are none, write none. f'(x) < 0 for x in 9. Give all values of a for which f'(x) exists and is positive. If there are none, write none. f'(x) > 0 for x in B 10. Which of the following choices best described the concavity of f(x)? Of(x) is concave up everywhere Of(x) is concave up in some places and concave down in other places Of(x) is concave down everywhere 11. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include: ⚫ correct locations for all intercepts and asymptotes • labels of any x-values where the function's derivative is 0 or undefined ⚫ correct intervals of increase and decrease, and labels of any places where they change ⚫ correct concavity, and labels of any places where it changes ? f(x) = log (5+ e*). Remark: WeBWorK won't be grading your sketch, but a grader on an exam might. It is therefore highly recommended that you do actually make a sketch while working on this problem.
In this question, we'll gather information for sketching the function 1. For which values of a is f(x) continuous? f(x) is continuous for a in the interval 2. Where does this function cross the x-axis? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. x = 3. Where does this function cross the y-axis? f(0) = 4. Does f(x) have any horizontal asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Horizontal asymptote(s) at y = 5. Does f(x) have any vertical asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none. Vertical asymptote(s) at x = 6. For large positive values of x, which function below is f(x) asymptotic to? For large positive x, f(x) = ○1 ○ ea ○ log(2) Ox 7. Find the first and second derivatives of f(x). f'(x) = f" (x) = # 8. Give all values of x for which f'(x) exists and is negative. If there are none, write none. f'(x) < 0 for x in 9. Give all values of a for which f'(x) exists and is positive. If there are none, write none. f'(x) > 0 for x in B 10. Which of the following choices best described the concavity of f(x)? Of(x) is concave up everywhere Of(x) is concave up in some places and concave down in other places Of(x) is concave down everywhere 11. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include: ⚫ correct locations for all intercepts and asymptotes • labels of any x-values where the function's derivative is 0 or undefined ⚫ correct intervals of increase and decrease, and labels of any places where they change ⚫ correct concavity, and labels of any places where it changes ? f(x) = log (5+ e*). Remark: WeBWorK won't be grading your sketch, but a grader on an exam might. It is therefore highly recommended that you do actually make a sketch while working on this problem.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.7: Functions Defined By Equations
Problem 1WE
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Transcribed Image Text:In this question, we'll gather information for sketching the function
1. For which values of a is f(x) continuous?
f(x) is continuous for a in the interval
2. Where does this function cross the x-axis? If there is more than one answer, enter a list of numbers; if there are no answers, enter none.
x =
3. Where does this function cross the y-axis?
f(0) =
4. Does f(x) have any horizontal asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none.
Horizontal asymptote(s) at y =
5. Does f(x) have any vertical asymptotes? If there is more than one answer, enter a list of numbers; if there are no answers, enter none.
Vertical asymptote(s) at x =
6. For large positive values of x, which function below is f(x) asymptotic to?
For large positive x, f(x) =
○1
○ ea
○ log(2)
Ox
7. Find the first and second derivatives of f(x).
f'(x) =
f" (x) =
#
8. Give all values of x for which f'(x) exists and is negative. If there are none, write none.
f'(x) < 0 for x in
9. Give all values of a for which f'(x) exists and is positive. If there are none, write none.
f'(x) > 0 for x in
B
10. Which of the following choices best described the concavity of f(x)?
Of(x) is concave up everywhere
Of(x) is concave up in some places and concave down in other places
Of(x) is concave down everywhere
11. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include:
⚫ correct locations for all intercepts and asymptotes
• labels of any x-values where the function's derivative is 0 or undefined
⚫ correct intervals of increase and decrease, and labels of any places where they change
⚫ correct concavity, and labels of any places where it changes
?
f(x) = log (5+ e*).
Remark: WeBWorK won't be grading your sketch, but a grader on an exam might. It is therefore highly recommended that you do actually make a sketch while working on this problem.
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