If y=3 is a horizontal asymptote of a rational function, which must be true?
lim
x→ 3
f(x) = 0
lim
x→ 0
f(x) = 3 **my answer
lim
x→ ∞
f(x) = 3
lim
x→ 3
f(x) = ∞
no, it is
lim
x→ ∞
f(x) = 3
your choice would simply be the point (0,3)
The correct answer is:
lim
x→ ∞
f(x) = 3
To determine if y=3 is a horizontal asymptote of a rational function, we need to evaluate the limit of the function as x approaches either positive or negative infinity, as well as the limit as x approaches any other value, such as 3.
In this case, we are given that y=3 is a horizontal asymptote. This means that as x approaches positive or negative infinity, the function approaches a value of 3.
So, to find the correct answer, we need to evaluate the limit of the function as x approaches 0, as x approaches 3, and as x approaches positive or negative infinity.
The correct answer must satisfy the condition that as x approaches 3, the limit of the function is 3.
Let's evaluate each of the options:
1. lim{x→3} f(x) = 0
2. lim{x→0} f(x) = 3 **my answer
3. lim{x→∞} f(x) = 3
4. lim{x→3} f(x) = ∞
Therefore, the correct answer is the second option: lim{x→0} f(x) = 3.