Question

Which of the following describes the end behavior of f(x) = (1/2)^x

Answer 1

Answer:

as x approaches infinity, f(x) approaches 0

as x approaches -infinity, f(x) approaches infinity

Step-by-step explanation:

we can observe that 1/2 < 1 and since it's being exponentiated, the f(x) gets smaller and smaller as x gets bigger.

For example, f(0) = 1, f(1) = 1/2, f(2) = 1/4

so, as x approaches an infinitely large number, f(x) gets closer and closer to zero.

this is the opposite as x approaches a negatively large number. following exponential rules, 1/2^(x) = 2^x for all x < 0. therefore as x approaches negative infinity, f(x) approaches infinity.

in this case, f(-1) = 2, f(2) = 4, f(3) = 8