Question

The graph of g(x)=(0.75)x+2 is shown.

Which equation is an asymptote of this function?

y = 3
y = 2
y=−2
y=−1

Answer 1

we are given

$f(x)=(0.75)^x+2$

For finding asymptote , we can find limit

$\lim_{x \to \infty} f(x)= \lim_{x \to \infty}((0.75)^x+2)$

$\lim_{x \to \infty} f(x)= \lim_{x \to \infty} (0.75)^x+\lim_{x \to \infty} 2)$

now, we can solve it

$\lim_{x \to \infty} f(x)= 0+2$

$\lim_{x \to \infty} f(x)= 2$

so, horizontal asymptote is

$y= 2$.............Answer