Answer:
[tex]\lim_{x\to -\infty} f(x)=\infty,\\\lim_{x\to \infty} f(x)=2,[/tex]
Step-by-step explanation:
The end behaviors of a function simply denote where the function is headed at x approaches negative and positive infinity. In [tex]f(x)=\left(\frac{1}{3}\right)^x+2[/tex], as [tex]x[/tex] gets approaches [tex]-\infty[/tex], the function will approach [tex]y=\infty[/tex]. As [tex]x[/tex] approaches [tex]\infty[/tex], the function will approach [tex]y=2[/tex].
We can write this in the following format to denote these end behaviors:
[tex]\lim_{x\to -\infty} f(x)=\infty,\\\lim_{x\to \infty} f(x)=2,[/tex]
