Question

State the end behavior of the function. For f(x)equals 3/x+2+5

(A) f(x) → +∞o as x→ +∞0; f(x) → +∞o as x→→∞
(B) f(x)→→∞ as x→ +∞o; f(x) →→∞ as x→-00
(C) f(x)→→∞o as x→ +∞0; f(x) → +∞o as x→→∞
(D) f(x) - → +∞o as x→→ +∞0; f(x)→→∞o as x →→∞

Answer 1

The end behavior of the given function f(x) = 3/(x+2) + 5 is that f(x) approaches 5 as x approaches positive infinity and negative infinity.

Step-by-step explanation:

The given function is f(x) = 3/(x+2) + 5. To determine the end behavior of the function, we need to evaluate the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the denominator x+2 becomes extremely large, causing the fraction 3/(x+2) to approach zero. Therefore, f(x) approaches 5 as x approaches positive infinity.

As x approaches negative infinity, the denominator x+2 becomes extremely large in absolute value, causing the fraction 3/(x+2) to approach zero. Therefore, f(x) approaches 5 as x approaches negative infinity.

So, the end behavior of the function f(x) is f(x) → 5 as x → ∞.