Question

Which of the following functions has the same horizontal asymptote as the function graphed below?

f(x)=-3^x+2 +2

f(x)=2^x-3

f(x)=3^x+2 -2

f(x)=2^x+2 -3

Answer 1

The functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) =
`2^(x) - 3` and

f(x) =
`2^((x+2)) -3`

Explanation:

The function that is graphed has horizontal asymptote as y = -3 .

As x → -∞ f(x) → - 3 for the second and fourth function. Hence the functions which has the same horizontal asymptote y = -3 as given in the graph are,

f(x) =
`2^(x) - 3` and

f(x) =
`2^((x+2)) -3`