Question

Find the horizontal asymptote for y= 5x/x+6 .
y = 0
y = −6
none
y = 5

Answer 1

`y = 5`

Explanation:

Given function:

`y=(5x)/(x+6)`

`\implies y=5 \left( (x)/(x+6)\right)`

`\textsf{As }x \rightarrow +\infty, \ (x)/(x+6) \rightarrow1`

`\implies y\rightarrow5`

`\textsf{As }x \rightarrow -\infty, \ (x)/(x+6) \rightarrow1`

`\implies y\rightarrow5`

As
`x` approaches infinity and negative infinity,
`y` approaches 5 (but never gets there). Therefore, the horizontal asymptote is
`y=5`