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Social Science2.5-x2For the given rational function f(x) =x2-4(A) Find any intercepts for the graph.(B) Find any vertical and horizontal asymptotes for the graph.(C) Graph the function in a standard viewing window using a graphing calculator.(A) Identify the x-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.The x-intercept(s) is(are) x =(Type an exact answer. Use a comma to separate answers as needed.)B. There are no x-intercepts.Identify the y-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The y-intercept(s) is(are) y =(Type an exact answer. Use a comma to separate answers as needed.)B. There are no y-intercepts.(B) Identify the vertical asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.A. There is one vertical asymptote. Its equation isB. There are two vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes areandO C. There are three vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes are, andD. There are no vertical asymptotes.Identify the horizontal asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choiceА.у3B. There is no horizontal asymptote.(C) Graph the function in a standard viewing window using a graphing calculator. All of the graphs have the same window size [10,10,1] by [ 10,10,1. Choose the correct answer below.O C.ов.А.D.
Can you help with this problem step by step?
![2.
5-x2
For the given rational function f(x) =
x2-4
(A) Find any intercepts for the graph.
(B) Find any vertical and horizontal asymptotes for the graph.
(C) Graph the function in a standard viewing window using a graphing calculator.
(A) Identify the x-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The x-intercept(s) is(are) x =
(Type an exact answer. Use a comma to separate answers as needed.)
B. There are no x-intercepts.
Identify the y-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept(s) is(are) y =
(Type an exact answer. Use a comma to separate answers as needed.)
B. There are no y-intercepts.
(B) Identify the vertical asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. There is one vertical asymptote. Its equation is
B. There are two vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes are
and
O C. There are three vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes are
, and
D. There are no vertical asymptotes.
Identify the horizontal asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
А.
у3
B. There is no horizontal asymptote.
(C) Graph the function in a standard viewing window using a graphing calculator. All of the graphs have the same window size [
10,10,1] by [ 10,10,1. Choose the correct answer below.
O C.
ов.
А.
D.](https://prod-qna-question-images.s3.amazonaws.com/qna-images/question/1083a8a9-0552-4d17-9464-fd309f4079b6/71f365d4-d335-47f7-84da-d2e192b19eac/ef58kzh.png)
Image Transcriptionclose
2. 5-x2 For the given rational function f(x) = x2-4 (A) Find any intercepts for the graph. (B) Find any vertical and horizontal asymptotes for the graph. (C) Graph the function in a standard viewing window using a graphing calculator. (A) Identify the x-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is(are) x = (Type an exact answer. Use a comma to separate answers as needed.) B. There are no x-intercepts. Identify the y-intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is(are) y = (Type an exact answer. Use a comma to separate answers as needed.) B. There are no y-intercepts. (B) Identify the vertical asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. There is one vertical asymptote. Its equation is B. There are two vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes are and O C. There are three vertical asymptotes. In order from left to right on the graph of the function, the equations of the vertical asymptotes are , and D. There are no vertical asymptotes. Identify the horizontal asymptotes, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice А. у3 B. There is no horizontal asymptote. (C) Graph the function in a standard viewing window using a graphing calculator. All of the graphs have the same window size [ 10,10,1] by [ 10,10,1. Choose the correct answer below. O C. ов. А. D.
Expert Answer
The given function is
Image Transcriptionclose
5-r f(x) -4
To find:
- Intercepts for the graph if exists.,
- The vertical and horizontal asymptotes for the graph.
- The graph for the function.
- The x-intercepts for the function can be found by substitu...
Image Transcriptionclose
5-x2 f(x) x2-4 5-x2 = 0 gives x2-4 Therefore x t2.236 (2.236, 0) and (-2.236,0) Hence, the x-intercepts for the function are
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Calculus
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