Question

Select the correct answer.

What is the equation of the asymptote for this function?
f(x) = (1/2)^x + 3

A. X=0
B.y=0
C.x = 3
D. y=3

Answer 1

To find the equation of the asymptote for the function f(x) = (1/2)^x + 3, determine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, the term (1/2)^x approaches 0 because any positive number raised to a negative power tends to zero. Therefore, the function approaches 0 + 3 = 3.

As x approaches negative infinity, the term (1/2)^x becomes extremely large (approaching positive infinity), resulting in a value much greater than 3. Therefore, the function also approaches 3 as x approaches negative infinity.

Hence, the equation of the asymptote for this function is y = 3. Therefore, the correct option is D. Y=3

Answer 2

D, explanation: although B seems correct, D is more correct since it directly affects the graph. Algebraicly, plug in 3 for y to get 3=(1/2)^x+3 subtracting 3 gives us a zero, and an exponent cannot equal zero. B is -3=(1/2)^x and this particular exponent cannot equal a negative since the base is positive. If possible choose both, but D would be better if you could only choose one