Question

Find the (D) (R) & (A)

Answer 1

Answer: Choice C

• domain = (-infinity, infinity)
• range = (-infinity, 0)
• horizontal asymptote is y = 0

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Explanation:

Since no division by zero errors are possible, and other domain restricting events are possible, we can plug in any x value we want. This means the domain is the set of all real numbers. Representing this in interval notation would be (-infinity, infinity).

The range is the set of negative real numbers, which when written in interval notation would be (-infinity, 0). This is because y = 5^x has a range of positive real numbers, and it flips when we negate the 5^x term. The graph of y = -5^x extends forever downward, and the upper limit is y = 0.

It never reaches y = 0 itself, so this is the horizontal asymptote. Think of it like an electric fence you can get closer to but can't touch.