we are given
[tex] g(x)=(0.5)^x+4 [/tex]
we can see that
there is no value of x for which g(x) is not defined
so, no vertical asymptote exists
now, we will find horizontal asymptote
[tex] \lim_{x \to \infty} g(x)= \lim_{x \to \infty}((0.5)^x+4 ) [/tex]
[tex] \lim_{x \to \infty} g(x)= (\lim_{x \to \infty} (0.5)^x+\lim_{x \to \infty} 4 ) [/tex]
[tex] \lim_{x \to \infty} g(x)= 0+4 [/tex]
so, we get
horizontal asymptote as
[tex] y= 4 [/tex]............Answer
