In this question, we'll gather information for sketching the function f(x) = 1 = ( 12/14+7) 13. Ꮖ 1. For which values of x is f(x) continuous? f(x) is continuous for x in the interval (0, Inf) U(-Inf, 0) 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 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 = 7^(1/3) 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 = 0 5. Find the first derivative of f(x). f'(x) = 1/3 (21/x+7)^(-2/3)*(-(21)/(x^(2))) 6. 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 (-0,0)(0,∞) 7. Give all values of x for which f'(x) exists and is positive. If there are none, write none. f'(x) > 0 for x in none 8. What is the best description of the curve y = it exists and has a vertical tangent line f(x) at x = -3? 9. What is the best description of the curve y = f(x) at x=0? it has an infinite discontinuity 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.
In this question, we'll gather information for sketching the function f(x) = 1 = ( 12/14+7) 13. Ꮖ 1. For which values of x is f(x) continuous? f(x) is continuous for x in the interval (0, Inf) U(-Inf, 0) 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 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 = 7^(1/3) 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 = 0 5. Find the first derivative of f(x). f'(x) = 1/3 (21/x+7)^(-2/3)*(-(21)/(x^(2))) 6. 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 (-0,0)(0,∞) 7. Give all values of x for which f'(x) exists and is positive. If there are none, write none. f'(x) > 0 for x in none 8. What is the best description of the curve y = it exists and has a vertical tangent line f(x) at x = -3? 9. What is the best description of the curve y = f(x) at x=0? it has an infinite discontinuity 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.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.2: Graphs Of Functions
Problem 1E: To graph the function f, we plot the points (x,) in a coordinate plane. To graph f(x)=x22, we plot...
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it says that part 6 is wrong. Please fix it and give me the correct answer
Transcribed Image Text:In this question, we'll gather information for sketching the function
f(x) =
1 = ( 12/14+7) 13.
Ꮖ
1. For which values of x is f(x) continuous?
f(x) is continuous for x in the interval (0, Inf) U(-Inf, 0)
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
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 = 7^(1/3)
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 = 0
5. Find the first derivative of f(x).
f'(x) = 1/3 (21/x+7)^(-2/3)*(-(21)/(x^(2)))
6. 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 (-0,0)(0,∞)
7. Give all values of x for which f'(x) exists and is positive. If there are none, write none.
f'(x) > 0 for x in none
8. What is the best description of the curve y =
it exists and has a vertical tangent line
f(x) at x = -3?
9. What is the best description of the curve y =
f(x) at x=0?
it has an infinite discontinuity
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.
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