Question

Identify the vertical asymptotes of f(x) = quantity x plus 6 over quantity x squared minus 9x plus 18.

Answer 1

Answer:

The vertical asymptotes are at x = 3 and x = 6.

Step-by-step explanation:

f ( x ) = ( x + 6 ) / ( x² - 9 x + 18 )

The denominator: x² - 9 x + 18 = x² - 6 x - 3 x + 18 = x ( x - 6 ) - 3 ( x - 6 ) =

= ( x - 6 ) · ( x - 3 ).

So the possible vertical asymptotes are at x = 3 and x = 6.

lim ( as x approaches 3 from the left side ) f ( x ) = +∞

lim ( x → 3 from the right side ) f ( x ) = -∞

lim ( x → 6 from the left side ) f ( x ) = -∞

lim ( x → 6 from the right side ) f ( x ) = +∞

So x = 3 and x = 6 are the vertical asymptotes.