Question

Which statement is true about the domain of y = 3(2^-x)? Explain.

The domain is all real numbers greater than or equal to 2.
The domain is all real numbers greater than 0
The domain is all real numbers
The domain is all real numbers less than 0

Answer 1

We want to determine the domain of ${y=3 \cdot 2^{-x}=3 \cdot ({2^{-1}})^x=3 \cdot ({ \frac{1}{2}})^x$

any function of the form $y=f(x)=a \cdot b^x$ is called an "exponential function",
the only condition is that b is positive and different from 1, and a is a nonzero real number.

The domain of such functions is all real numbers.

That is for any x, the expression 3(2^-x) "makes sense".



Answer: The domain is all real numbers