State domain and range of y=2^x-3+3

Question

State domain and range of y=2^x-3+3?

Last three is not an exponent only x and the first three are.

Answer 1

Hi Jazzy,

 

The domain is the set of values  x can take on and for this expression x can be any real number

 

The range is the values that y can take on and for this expression y will be any value >3

 

You might (should) ask why that is the case.

 

OK, glad you asked.

 

when x equals 3 the exponent will be 0  (x-3)=0  and 2⁰  =1

 

so y = 1 + 3  = 4

 

when x is less than 3 the exponent will be negative and as x moves more negative the value of 2^(x-3)

 

will be a fraction that gets increasingly smaller.  For example 2^-1 =1/2,  2^-4 = 1/16  and 1/16 is less than one half.

 

The result will approach 0 but never quite get there and therefore

 

the overall expression will approach 3 but never quite get there

 

Hope this helps