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