Question

Given f(x) = 200. (1.05) and g(x) = 600, write a function h(x) to represent the sum 6) - 50) + g(x).

Then identify the horizontal asymptote of h(x).
A. h(x)=200⋅(1.05)ˣ−50+600, horizontal asymptote: none

B. h(x)=200⋅(1.05) ˣ+600−50, horizontal asymptote: none

C. ℎ(x)=200⋅(1.05) ˣ+600−50, horizontal asymptote:y=600
D. h(x)=200⋅(1.05) ˣ−50+600, horizontal asymptote: y=600

Answer 1

Function h(x) represents the sum of f(x) and g(x) minus 50, and is expressed as h(x)=200·(1.05)x+600-50. As x approaches infinity, the exponential term causes h(x) to increase indefinitely, implying there is no horizontal asymptote.

Step-by-step explanation:

The task is to write a function h(x) representing the sum of f(x) and g(x) minus 50, and then identify the horizontal asymptote of h(x). Given the functions f(x) = 200 · (1.05)x and g(x) = 600, the function h(x) will be h(x) = 200 · (1.05)x - 50 + 600.

Now, we simplify the equation of h(x) as follows: h(x) = 200 · (1.05)x + 600 - 50. As x approaches infinity, the term 200 · (1.05)x grows without bound, but the constant term remains the same. Therefore, h(x) does not have a horizontal asymptote. The correct answer is B: h(x)=200·(1.05)x+600-50, horizontal asymptote: none.