Question

The graph of g(x)=(0.5)x+4 is shown. Which equation is an asymptote of this function? y = 0 y = 4 x = 4 x = 0

Answer 1

we are given

$g(x)=(0.5)^x+4$

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

$\lim_{x \to \infty} g(x)= \lim_{x \to \infty}((0.5)^x+4 )$

$\lim_{x \to \infty} g(x)= (\lim_{x \to \infty} (0.5)^x+\lim_{x \to \infty} 4 )$

$\lim_{x \to \infty} g(x)= 0+4$

so, we get

horizontal asymptote as

$y= 4$............Answer