Answer: The end behavior of (f - g)(x) can be found by analyzing the end behavior of f(x) and g(x).
As x approaches infinity, both f(x) and g(x) approach some constant value. Specifically, f(x) approaches infinity/4 = 0 and g(x) approaches 3/2.
Therefore, the end behavior of (f - g)(x) as x approaches infinity is:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = x/4 - 3/2
(f - g)(x) = (x - 6)/4
As x approaches infinity, the numerator of (f - g)(x) (x - 6) will approach infinity, while the denominator (4) will remain constant. Therefore, the end behavior of (f - g)(x) as x approaches infinity is:
(f - g)(x) approaches infinity/4 = 0
Similarly, as x approaches negative infinity, both f(x) and g(x) approach some constant value. Specifically, f(x) approaches negative infinity/4 = 0 and g(x) approaches 3/2.
Therefore, the end behavior of (f - g)(x) as x approaches negative infinity is:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = x/4 - 3/2
(f - g)(x) = (x - 6)/4
As x approaches negative infinity, the numerator of (f - g)(x) (x - 6) will approach negative infinity, while the denominator (4) will remain constant. Therefore, the end behavior of (f - g)(x) as x approaches negative infinity is:
(f - g)(x) approaches negative infinity/4 = 0
So, the end behavior of (f - g)(x) is that it approaches 0 as x approaches either infinity or negative infinity.
Explanation: