Question

Use the graph of the function y = 4x to answer the following questions.

The domain of the function is
✔ negative infinity

to
✔ positive infinity

because an exponent can be any real number.

The range of the function is

to

because 4x is always positive.

Answer 1

The domain and range of the function y = 4^x are all real numbers for the domain and positive real numbers for the range, excluding zero.

Step-by-step explanation:

When considering the function y = 4x, the domain is all real numbers, which means it extends from negative infinity to positive infinity, because the exponent, in this case x, can indeed be any real number. The range of the function, however, is strictly positive because the base of the exponent, which is 4, is a positive number; therefore, no matter what real number x is, the output y will always be positive. This excludes zero and negative numbers, hence the range of y = 4x is from 0 to positive infinity.