Question

80 pts! please correct answer

What is the end behavior of this radical function?
f(x)=4\sqrt{x-6 }

A.
As x approaches positive infinity, f(x) approaches positive infinity.
B.
As x approaches negative infinity, f(x) approaches positive infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches negative infinity, f(x) approaches negative infinity.

Answer 1

Explanation:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞x→∞.

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

Answer 2

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

Explanation:

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)

x→∞ x→∞

= 4√(lim(x-6))

x→∞

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞

x→∞

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.