You can put this solution on YOUR website! What is the domain and range of the following function.
If the exponent is supposed to be x+1 instead of x, let me know and I'll edit this.
The domain of exponential functions is ALL REAL NUMBERS because there are no restrictions on the value of x.
Interval Notation: (-infinity, infinity)
Set builder Notation: {x|x=R}
:
The range, you have to think about. There is no power that you can raise something to that will make it =0 or change its sign. 2^x will get close to, but never be 0. The - infront tells you that the function declines exponentially. The +1 tells us that the highest this function will get close to is 1. Therefore the range is:
Interval notation: (1,-infinity)
Set Builder Notation: {y|y<1}
:
If you're allowed to use a graphing calculator, look at the graph:
It goes forever left and right, therefore the domain is all real numbers.
The highest it approaches is y=1 and it shoots down to -infinity therefore the range is {y|y<1}
Happy Calculating!!!
(