we are given
[tex] f(x)=(0.75)^x+2 [/tex]
For finding asymptote , we can find limit
[tex] \lim_{x \to \infty} f(x)= \lim_{x \to \infty}((0.75)^x+2) [/tex]
[tex] \lim_{x \to \infty} f(x)= \lim_{x \to \infty} (0.75)^x+\lim_{x \to \infty} 2) [/tex]
now, we can solve it
[tex] \lim_{x \to \infty} f(x)= 0+2 [/tex]
[tex] \lim_{x \to \infty} f(x)= 2 [/tex]
so, horizontal asymptote is
[tex] y= 2 [/tex].............Answer
