Determine the domain and range of the following function. Record your answers in set notation. State the family of functions to which it belongs. a) The domain is x ∈ R , and t…

Question

Determine the domain and range of the following function. Record your answers in set notation. State the family of functions to which it belongs.

a) The domain is x ≥ −100 , and the range is all real numbers. The function is a quartic function.
b) The domain is x ≥ −100 , and the range is all real numbers. The function is an exponential function.
c) The domain is all real numbers, and the range is y ≥ −100 . The function is a quartic function.
d) The domain is all real numbers, and the range is y ∈ R . The function is an exponential function.

Answer 1

The domain is all real numbers, and the range is y ∈ R . The function is an exponential function

Step-by-step explanation:

Let's analyze the options provided:

a) The domain is x ≥ −100 which means the function is defined for all real numbers greater than or equal to -100. The range is stated to be all real numbers. This suggests a quartic function,, where the highest power of x is 4.

b) The domain is x ≥ −100 and the range is all real numbers. This does not align with an exponential function. Exponential functions typically have a domain of all real numbers and a range of positive real numbers or zero.

c) The domain is all real numbers and the range is y ∈ R . This is similar to an exponential function where the range covers all real numbers greater than or equal to a certain value, but the given domain doesn't align with an exponential function.

d) The domain is all real numbers and the range is y ∈ R . This matches the characteristics of an exponential function, where the domain covers all real numbers and the range spans values greater than or equal to a certain value, in this case, -100.

Thus, option d) appears to be the correct choice: The domain is all real numbers, and the range is y ≥ −100. The function belongs to the family of exponential functions.