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(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?

f(x) is negative for all x < –3
f(x) is negative for all x > –3
f(x) is positive for all x < 10
f(x) is positive for all x > 10

2 Answers

10 votes


\\ \rm\Rrightarrow y=(10)/(x^2-7x-10)

If we factor


\\ \rm\Rrightarrow y=(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

User Mitchel Verschoof
by
8.4k points
11 votes

Answer:

f(x) is positive for all x > 10

Explanation:

Given function:


f(x)=(10)/(x^2-7x-30)

Asymptote

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)=(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)

(100 Points) Given f of x is equal to 10 divided by the quantity x squared minus 7x-example-1
User Yufei Zhao
by
8.1k points

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