Consider the following rationa
Consider the following rational function:
f(x) = 18 (x-1)/(x^2 – 9)
Which of the following are true?
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A. The function touches but does not cross the horizontal axisat: x= 1. |
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B. When x is very large and positive, the value of the f(x)approaches to zero. |
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C. The function cuddles up to the vertical lines which passthrough x = – 3 and x =3. |
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D. The function cuts the horizontal axis at x = 3 and x =-3. |
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E. The vertical intercept of the function is (0,2) and thehorizontal intercept is (1, 0). |
Answer:
Given,
A. Clearly, at 
, 
For 
,while for 
.Since the sign of the function changes at 
it crosses the horizontal axis at
————
B. When 
is large and positive, i.e. 
Thus, indeed 
approaches 0 when is very large and positive
————-
C. The poles of the function correspond to 
. which correspond to 
. Thus, it is true that the function cuddles up to the verticallines which pass through
————-
D. We have already seen that the function crosses the horizontalaxis only at . So this is not true.
————-
E. Vertical Intercept corresponds to 
. At
Thus, the vertical intercept is 
. We have already seen in (A) that the horizontal intercept is
. So this is true.
————–
Thus, the true statements are B,C,E
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