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:

$y=1$