Question

Summarize the pertinent information obtained by applying the graphing

strategy and sketch the graph of f(x)=-2x/(x-1)^2

Part 1: Find the​ x-intercepts of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.The​ x-intercept(s) is/are at x=____. ​(Type an integer or a decimal. Use a comma to separate answers as​ needed.)

B. There are no​ x-intercepts.

Part 2. Find the​ y-intercepts of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.The​ y-intercept(s) is/are at y=_____. ​(Type an integer or a decimal. Use a comma to separate answers as​ needed.)

B. There are no​ y-intercepts.

Part 3. Find any horizontal asymptotes of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer​box(es) to complete your choice.

A. The function has one horizontal​ asymptote, ____ ​(Type an​ equation.)

B. The function has two horizontal asymptotes. The top asymptote is ____ and the bottom asymptote is___. ​(Type equations.)

C. There are no horizontal asymptotes.

Part 4. Find any vertical asymptotes of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer​box(es) to complete your choice.

A. The function has one vertical​ asymptote,____. ​(Type an​ equation.)

B. The function has two vertical asymptotes. The leftmost asymptote is_____ and the rightmost asymptote is ______. ​(Type equations.)

C. There are no vertical asymptotes.

Part 5. Find the intervals where​ f(x) is increasing or decreasing. Select the correct choice below and fill in the answer​box(es) to complete your choice.

A. The function is increasing on____. It is never decreasing. ​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)

B. The function is increasing on______ It is decreasing on______. ​(Type your answers in interval notation. Use a comma to separate answers as​ needed.)

C. The function is decreasing on_____. It is never increasing.

Part 6. Find the location of any local extrema of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer​box(es) to complete your choice.

A. There is a local maximum at x=______. and there is a local minimum at x=_____. ​(Type integers or decimals. Use a comma to separate answers as​needed.)

B. There is a local maximum at x=____. There is no local minimum. ​(Type an integer or a decimal. Use a comma to separate answers as​ needed.)

C.There is a minimum at x=____. There is no local maximum. ​(Type an integer or a decimal. Use a comma to separate answers as​ needed.)

D. There are no local extrema. ​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)

Part 7. Find the intervals where​ f(x) is concave upward or downward. Select the correct choice below and fill in the answer​box(es) to complete your choice.

A. The function is concave upward on____ It is never concave downward. ​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)

B. The function is concave upward on_____It is concave downward on_____. ​(Type your answers in interval notation. Use a comma to separate answers as​ needed.)

C. The function is concave downward on_____ It is never concave upward. ​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)

Part 8. Find the location of any inflection points of​ f(x). Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.There​ is/are (a) inflection​ point(s) at x=_____. ​(Type an integer or a decimal. Use a comma to separate answers as​ needed.)

B. There are no inflection points.

Answer 1