Identify the vertical asymptotes of f(x) = 10 over quantity x squared minus 7x minus 30.

Solution:

Vertical asymptotes are defined as the straight line of the equation towards the function f (x). 

It is given that

f(x) = 10 over quantity x squared minus 7x minus 30

We can write it as

f(x) = 10/ (x² - 7x - 30)

Let us take f(x) = 0

0 = 10/ (x² - 7x - 30)

Let us factor the denominator

x² - 7x - 30 = 0

Splitting the middle term

x² - 10x + 3x - 30 = 0

Taking out the common terms

x(x - 10) + 3(x - 10) = 0

(x + 3)(x - 10) = 0

x + 3 = 0 or x - 10 = 0

x = -3 or x = 10

Therefore, the vertical asymptotes are x = -3 or x = 10.

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Identify the vertical asymptotes of f(x) = 10 over quantity x squared minus 7x minus 30.

Summary:

The vertical asymptotes of f(x) = 10 over quantity x squared minus 7x minus 30 are x = -3 or x = 10.