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