Describe the end behavior of f(x) =
1
3
x - 5. [Note: This is an exponential function where
1
3
is the base and x is the exponent.]
A) As x → -∞, f(x) → -5. As x → ∞, f(x) → ∞.
B) As x → -∞, f(x) → 0. As x → ∞, f(x) → ∞.
C) As x → -∞, f(x) → ∞. As x → ∞, f(x) → -5.
D) As x → -∞, f(x) → ∞. As x → ∞, f(x) → 0
i think the answer is d
If you mean (1/3)^(x-5)
then you are correct.
To determine the end behavior of the given exponential function f(x) = (1/3)^(x - 5), we need to analyze what happens to the function as x approaches positive and negative infinity.
First, let's consider what happens as x approaches negative infinity (x → -∞). In this case, we have:
f(x) = (1/3)^(x - 5)
As x becomes infinitely negative, the exponent (x - 5) also becomes infinitely negative. When a positive base (1/3 in this case) is raised to an infinitely negative exponent, the value approaches 0. Therefore, as x → -∞, f(x) approaches 0.
Now, let's consider what happens as x approaches positive infinity (x → ∞). In this case, we have:
f(x) = (1/3)^(x - 5)
As x becomes infinitely positive, the exponent (x - 5) also becomes infinitely positive. When a positive base (1/3 in this case) is raised to an infinitely positive exponent, the value approaches infinity. Therefore, as x → ∞, f(x) approaches infinity.
Based on our analysis, the correct answer is:
B) As x → -∞, f(x) → 0. As x → ∞, f(x) → ∞.