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wariber [46]
2 years ago
6

(100 Points) Given f of x is equal to 10 divided by the quantity x squared minus 7x minus 30, which of the following is true?

Mathematics
2 answers:
ikadub [295]2 years ago
4 0

Answer:

f(x) is positive for all x > 10

Step-by-step explanation:

Given function:

f(x)=\dfrac{10}{x^2-7x-30}

<u>Asymptote</u>

Asymptote: a line which the curve gets infinitely close to, but never touches.

Factor the denominator of the function to find the vertical asymptotes:

\implies x^2-7x-30

\implies x^2-10x+3x-30

\implies x(x-10)+3(x-10)

\implies (x+3)(x-10)

Therefore:

f(x)=\dfrac{10}{(x+3)(x-10)}

The function is undefined when the denominator is equal to zero.

Therefore, there are vertical asymptotes at x = -3  and  x = 10
and a horizontal asymptote at y = 0

f(x) is positive for (10, ∞)

f(x) is negative for (-3, 10)

f(x) is positive for (-∞, -3)

katrin2010 [14]2 years ago
3 0

\\ \rm\Rrightarrow y=\dfrac{10}{x^2-7x-10}

If we factor

\\ \rm\Rrightarrow y=\dfrac{10}{(x+3)(x-10)}

Horizontal Asymptotes

  • y=0 as there is no variable in numbers

Vertical asymptotes

solve the denominator for 0

  • x=-3
  • x=10

Henec option D is correct

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