Question

The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n+c. What does the attached graph tell you about the domain and the range of this function?. A. The domain is [c, ∞) & the range is [-k,∞). B. The domain is [-k,∞) & the range is (-∞,c]. C. The domain is (-∞,∞) & the range is (-∞,∞). D. The domain is (-∞,k] & the range is [c,∞).

Answer 1

A negative number raised to a certain power is equal to an undefined value. In this case, the goal of the have x equal to -k and numbers greater than it. Hence the domain includes k and numbers to infinity. The minimum value of the range is negative infinity up to a value where the first term is zero or range equal to c.Hence the answer is  B. The domain is [-k,∞) & the range is (-∞,c].

Answer 2

The attached graph tells me that the domain is [-k,∞) and the range of this function is (-∞,c]. The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query about this specific question.