There may be more than one correct answer. Select all answers that apply.
A)As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
B)As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.
C)As x→∞, f(x)→∞, and as x→−∞, f(x)−∞.
D)As x→∞, f(x)→∞, and as x→−∞, f(x)→∞.
B and D?
tough to say, with no information about f(x)
To determine which answers are correct, we need to understand the behavior of the function f(x) as x approaches positive and negative infinity.
Option A states that as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity.
Option B states that as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
Option C states that as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
Option D states that as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches positive infinity.
Let's analyze each option:
Option A is incorrect because it contradicts itself. It is not possible for a function to approach both negative and positive infinity simultaneously.
Option B is correct because it correctly states that as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
Option C is incorrect because it states that as x approaches positive infinity, f(x) approaches positive infinity, which contradicts the given function behavior.
Option D is incorrect because it states that as x approaches negative infinity, f(x) approaches positive infinity, which contradicts the given function behavior.
Therefore, the correct answers are B) As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.