Question

Which of the following could be an example of a function with a domain (-♾, ♾) and a range (-♾, 4)? Check all that apply.

A. v= -(0.25)^x+4
B. v= – (3)^x+4
C. v= -(3)^x-4
D. v= -(0.25)^x– 4

Answer 1

Of the given functions, only option A, which is an exponential decay function shifted up by 4, has a domain of (-∞, ∞) and a range of (-∞, 4].

Step-by-step explanation:

Considering the question, we are looking for functions that have a domain of (-∞, ∞) and a range of (-∞, 4]. We can analyze the proposed functions one by one.

• A. v= -(0.25)^x+4: This function is an exponential decay function due to the base 0.25 being between 0 and 1. As x approaches ∞, v approaches 4, and as x approaches -∞, v approaches -∞. So, the range of this function is indeed (-∞, 4], which means it fits the criteria.

• B. v= – (3)^x+4: This function is an exponential growth function with a base greater than 1. It increases without bound as x increases, which means it does not fit the criteria since the range exceeds 4.

• C. v= –(3)^x-4: Similarly to option B, this is an exponential growth function, but it is translated 4 units down. The range for this function extends below -4, which does not meet the specified range requirement.

• D. v= –(0.25)^x– 4: This is another exponential decay function like option A but shifted down by 4 units. As x approaches ∞, v approaches -4, and as x approaches -∞, v approaches -∞, making the range (-∞, -4), which is not within the specified range.

Therefore, only option A fits the given domain and range criteria.