Answer:
- domain: x > -2
- range: -∞ < y < ∞
Explanation:
You want the domain and range of the function f(x) = -log₅(x +2).
Domain
The domain is the horizontal extent of the graph, the set of x-values for which the function is defined.
The function log(x) is undefined for x ≤ 0. It its application here, we require ...
(x +2) > 0
x > -2 . . . . . . . . the domain of f(x)
Range
The range is the vertical extent of the graph, the set of values the function may produce.
The log function may have any value. Its range is "all real numbers."
-∞ < y < ∞ . . . . . . . . . the range of f(x)
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Additional comment
The leading minus sign, and the base of the logarithm serve to scale the graph vertically. They have no effect on the domain or range.
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