Question

Not sure how to solve this

Answer 1

The function f(x) = -7 *
`2^x` + 5 has a horizontal asymptote of
`\(y = -\infty\)` as x approaches positive infinity and y = 5 as x approaches negative infinity.

What is the asymptote of a function?

To determine the asymptote of the function f(x) = -7 *
`2^x` + 5, we need to consider the behavior of the function as x approaches positive or negative infinity.

In this case, the function is an exponential function with a base of 2. As x approaches positive infinity, the term
`2^x` becomes very large, and since there is a negative coefficient in front of it, the entire function will tend towards negative infinity. Therefore, the horizontal asymptote is
`y = -\infty`.

On the other hand, as x approaches negative infinity,
`2^x` becomes very small, and the function will be dominated by the constant term 5. So, the horizontal asymptote is y = 5.