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 in the interval B 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. 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 = 4. 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= 5. Find the first derivative of f(x). f'(x) = 6. Give all values of a for which f'(x) exists and is negative. If there are none, write none. f'(x) < 0 for x in B 7. Give all values of a for which f'(x) exists and is positive. If there are none, write none. f'(x) 0 for a in B 8. What is the best description of the curve y = f(x) at x = -3? ? 9. What is the best description of the curve y = f(x) at x = 0? ? 10. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include: ⚫ correct locations for all discontinuties, intercepts, and asymptotes; • labels of any x-values where the function's derivative is 0 or undefined, with the appropriate behaviour sketched; ⚫ correct intervals of increase and decrease. Your graph does not have to include labelled inflection points. ? 21 1/3 f(x) = (1 +7). 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 in the interval B 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. 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 = 4. 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= 5. Find the first derivative of f(x). f'(x) = 6. Give all values of a for which f'(x) exists and is negative. If there are none, write none. f'(x) < 0 for x in B 7. Give all values of a for which f'(x) exists and is positive. If there are none, write none. f'(x) 0 for a in B 8. What is the best description of the curve y = f(x) at x = -3? ? 9. What is the best description of the curve y = f(x) at x = 0? ? 10. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include: ⚫ correct locations for all discontinuties, intercepts, and asymptotes; • labels of any x-values where the function's derivative is 0 or undefined, with the appropriate behaviour sketched; ⚫ correct intervals of increase and decrease. Your graph does not have to include labelled inflection points. ? 21 1/3 f(x) = (1 +7). 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.
Chapter4: Rational Functions And Conics
Section4.1: Rational Functions And Asymptotes
Problem 4E: The graph of fx=1/x is a .
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solve it please
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 in the interval
B
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. 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 =
4. 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=
5. Find the first derivative of f(x).
f'(x) =
6. Give all values of a for which f'(x) exists and is negative. If there are none, write none.
f'(x) < 0 for x in
B
7. Give all values of a for which f'(x) exists and is positive. If there are none, write none.
f'(x) 0 for a in
B
8. What is the best description of the curve y = f(x) at x = -3?
?
9. What is the best description of the curve y = f(x) at x = 0?
?
10. Combine all of your answers to make a detailed sketch of y = f(x). Your sketch should include:
⚫ correct locations for all discontinuties, intercepts, and asymptotes;
• labels of any x-values where the function's derivative is 0 or undefined, with the appropriate behaviour sketched;
⚫ correct intervals of increase and decrease.
Your graph does not have to include labelled inflection points.
?
21
1/3
f(x) = (1 +7).
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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