Question 611825
Let's start with the {{{2^x}}}. Once one has worked with exponents and logarithms enough, you learn that a power of 2 (or any other positive number number) can result in <i>any</i> positive number! What a power of 2 can't be is zero or negative. So the {{{2^x}}} part can have  a value of any positive number.<br>
The minus in front of the {{{2^x}}} turns all those positive numbers negative. So {{{-2^x}}} can result in any negative number. IOW, any number less than zero.<br>
If you take all those numbers than zero and then add 2, you end up with all numbers less than 2. This is the range of your function: all numbers less than 2.