Question

Find the vertical asymptote(s) of f of x equals quantity 4 x squared plus 3x plus 6 end quantity over quantity x squared minus 36

Answer 1

The vertical asympototes of f(x) are  at x = -6 and x = 6

Step-by-step explanation:

To find the vertical asymptote(s) of a rational function,

• Equate the denominator by 0
• Solve it for x
• If x = a, then the vertical asymptote is at x = a

∵ $f(x)=\frac{4x^{2}+3x+6}{x^{2}-36}$

- Equate the denominator x² - 36 by 0

∵ x² - 36 = 0

- Add 36 to both sides

∴ x² = 36

- Take √ for both sides

∴ x = ± 6

∴ There are vertical asymptotes at x = -6 and x = 6

The vertical asympototes of f(x) are  at x = -6 and x = 6

Learn more:

You can learn more about the asymptotes in brainly.com/question/6459599

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