Question

The equation for an exponential function is r(x) = 2 · (0.75)x – 7. Which statement correctly describes the end behavior of the function?

As x → –∞, r(x) → ∞, and as x → ∞, r(x) → –7.
As x → –∞, r(x) → ∞, and as x → ∞, r(x) → 2.
As x → –∞, r(x) → –7, and as x → ∞, r(x) → ∞.
As x → –∞, r(x) → 2, and as x → ∞, r(x) → ∞.

Answer 1

Step-by-step explanation:

The correct statement that describes the end behavior of the function r(x) = 2 · (0.75)^x – 7 is:

As x → -∞, r(x) → -7, and as x → ∞, r(x) → ∞.

As x approaches negative infinity, the exponential term (0.75)^x becomes very close to zero, and the function approaches -7. As x approaches positive infinity, the exponential term becomes larger and larger, making the function approach positive infinity.