Answer:
I think your functions are [tex]y=2^{x}[/tex] ,[tex]y=2*5^{x}[/tex] and [tex]y=2+5^{x}[/tex]
If yes then then the third function which is [tex]y=2+5^{x}[/tex].
Step-by-step explanation:
The function [tex]c^{x}[/tex] where c is a constant has
Domain : [tex]c\geq 0[/tex]
Range : ( 0 , ∞ )
The above range is irrespective of the value of c.
I have attached the graph of each of the function, you can look at it for visualization.
- [tex]y=2^{x}[/tex] ⇒ This function is same as [tex]c^{x}[/tex] so its range is ( 0 , ∞ ).
- [tex]y=2*5^{x}[/tex] ⇒ If we double each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as ( 0 , ∞ ).
- [tex]y=2+5^{x}[/tex] ⇒ If we add 2 to each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as ( 2 , ∞ ).
