How do you find the asymptotes for #y = 4/(x - 3)#?

vertical asymptotes occur as the denominator of a rational function >tends to zero. To find the equation let the denominator = 0

solve : x - 3 = 0 → x = 3 is the equation

If the degree of the numerator is less than the degree of the denominator , as is the case here , then the equation is y = 0

here is the graph of the function as an illustration graph{4/(x-3) [-10, 10, -5, 5]}

To find the asymptotes of the function ( y = \frac{4}{x - 3} ), you need to determine the values of ( x ) for which the function becomes undefined, as these will be the vertical asymptotes. The vertical asymptote occurs where the denominator becomes zero, which in this case is when ( x - 3 = 0 ). Solve for ( x ) to find the vertical asymptote.

( x - 3 = 0 )
( x = 3 )

Therefore, the vertical asymptote is ( x = 3 ).

There are no horizontal asymptotes for this function.