Question

Identify the horizontal asymptote of the function below *y= 2* + 1O y=0O y=1O y=2O None of the above

Answer 1

`y=2^x+1`

Let's find the limit:

`\begin{gathered} \lim _(x\to-\infty)(2^x+1)=\lim _(x\to-\infty)2^x+\lim _(x\to-\infty)1 \\ where\colon \\ \lim _(x\to-\infty)2^x=2^{\lim _(x\to-\infty)x}=0 \\ so\colon \\ \lim _(x\to-\infty)(2^x+1)=1 \end{gathered}`

Therefore, the horizontal asymptote is:

`y=1`