Domain and range of f(x)=2(3)

Question

f(x)=2(3^x)

Answer 1

So, our domain is our input. Is there anything we can't put in as x? Certainly not, so our domain is all real numbers.

 

The range is the output. Let's pick some numbers to use for x and see what happens.

 

y = 3⁴

y = 81

 

y = 3^1/4

Well, I'm not doing that in my head, but it's the fourth root of 3.

 

y = 3⁰

y = 1

 

y = 3^-2

y = 1/9

 

Now, technically if we take an even root (square root, 4th root, ...) we get a positive and negative answer, but I'd say to ignore the negative for now.

 

Therefore, the smallest y-value we are going to come up with is 1, with no upper bound. 3¹²³ is a big number.

 

So, our range is y≥ 1.