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.