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 ({ (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