Question

Consider the following rational function:

f(x) = 18 (x-1)/(x^2 - 9)

Which of the following are true?

A. The function touches but does not cross the horizontal axis at: x= 1.
B. When x is very large and positive, the value of the f(x) approaches to zero.
C. The function cuddles up to the vertical lines which pass through x = - 3 and x =3.
D. The function cuts the horizontal axis at x = 3 and x = -3.
E. The vertical intercept of the function is (0,2) and the horizontal intercept is (1, 0).

Answer 1

Given,

A. Clearly, at ,

For , while for . Since the sign of the function changes at it crosses the horizontal axis at

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B. When is large and positive, i.e.

Thus, indeed approaches 0 when is very large and positive

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C. The poles of the function correspond to . which correspond to . Thus, it is true that the function cuddles up to the vertical lines which pass through

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D. We have already seen that the function crosses the horizontal axis only at . So this is not true.

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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.

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Thus, the true statements are B,C,E