Question

Find the horizontal asymptote of the following exponential function: f(x) = −3(2)ˣ−5:

a) y = 0
b) No horizontal asymptote
c) y = -5
d) y = [infinity]

Answer 1

The horizontal asymptote of the function f(x) = −3(2)^x−5 is y = -5, as that's the value the function approaches as x tends to infinity.

Step-by-step explanation:

To find the horizontal asymptote of the exponential function f(x) = −3(2)^x−5, we need to examine the behavior of the function as x tends to infinity. As x increases, the term −3(2)^x grows exponentially, but no matter how large it gets, the subtraction of 5 will always leave us with a resulting value that does not include the negative infinite term; thus, the function approaches the horizontal line y = −5 as x tends to plus or minus infinity. Therefore, the correct answer is c. y = -5.