Question

Identify the asymptotes.
y = 4 / 3x+15

Answer 1

Aasymptotes is a line that a curve approaches as it heads towards infinity

Answer 2

Now can you find points where this function will approach infinity?

Answer 3

I don't get it ._.

Answer 4

can you find value of x where y = 4 / 3x+15 approaches to infinity?

Answer 5

We know that as the denominator goes to \(0\), our whole expression will "blow up" and go off to infinity so let $$3x+15=0\\3x=-15\\x=-5$$hence we have a vertical asymptote at \(x=-5\). As \(x\to\pm\infty\) however the denominator gets very large in magnitude and so our expression will grow closer and closer to \(0\) so we have a horizontal asymptote at
\(y=0\).