Asymptote Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Identify all asymptotes of

h(x) = \dfrac{5}{x + 3}

1
Vertical: denominator zero when $x+3=0 \Rightarrow x = -3$ . Numerator $5 \neq 0$ , so vertical asymptote at $x = -3$ .
2
Horizontal: numerator degree (0) < denominator degree (1), so horizontal asymptote is $y = 0$ (the $x$ -axis).

Answer

Vertical asymptote:

x = -3

; Horizontal asymptote:

y = 0

When the numerator's degree is less than the denominator's, the function approaches zero for large

|x|

, giving a horizontal asymptote at

y=0

. The vertical asymptote marks where the function blows up.

About Asymptote

An asymptote is a line that a curve approaches arbitrarily closely as the input (or output) grows without bound, but typically never reaches.

Find the vertical and horizontal asymptotes of [formula].

Find the oblique (slant) asymptote of [formula].

For [formula], determine the horizontal asymptote and verify by computing [formula].