What is the domain and range of the function f(x) =a^x?

Question

a. Domain = negative real numbers range = negative real numbers

b. Domain=all real numbers range =all real numbers.

c. Domain =positive real numbers range= positive real numbers

d. Domain= real numbers range = positive real numbers

Answer 1

Pick any value for a and graph it on a graphing utility (like desmos or like your graphing calculator). Let's pick a = 2 so the function is f(x) = 2^x

Here is a table of some values:

x f(x)

---------

-2 1/4

-1 1/2

0 1

1 2

2 4

3 8

4 16

5 32

6 64

You can see that there is an unlimited possibility of x's you can pick, in fact x (the domain) can be any real number.

But the f(x) values (aka "y" values) are limited. Notice there are no negative numbers and, there isn't even a zero. So the Range must be all real numbers greater than zero.