The function f(x) has a vertical asymptote at x = 2 and the Horizontal Asymptotes is y = 0
Vertical Asymptotes
From the question, we have the following parameters that can be used in our computation:
f(x) = 3/(x - 2)
The denominator of the function, x - 2,
This means, that f(x) has a vertical asymptote at x = 2.
Behavior near the Vertical Asymptotes
As x approaches 2 from the left, f(x) approaches negative infinity.
As x approaches 2 from the right, f(x) approaches positive infinity.
Horizontal Asymptote
Here, the Horizontal Asymptotes is y = 0
This is so because the degree of the numerator is less than the degree of the denominator
End Behavior
As x approaches positive infinity, f(x) approaches 0.
As x approaches negative infinity, f(x) approaches 0.
Domain
The function f(x) is undefined when the denominator, x - 2, is equal to zero.
So, the domain of the function is all real numbers except for x = 2.
Range
The range of the function f(x) is all real numbers less than 0 and greater than or equal to 0.
This is because the function cannot take 0 as its value
Positive and Negative Intervals
The function f(x) is positive when x is greater than 2
The function f(x) is negative when x is less than 2