Answer:
[tex]y=5^{x}+2[/tex]
Step-by-step explanation:
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
To solve this problem, we have plotted each function and are shown in order below. As you can see:
[tex]y=2^x \\ \\ y=2(5^x) \ and \ y=5^{x+2}[/tex]
have the same range [tex](0, +\infty)[/tex]. The only graph that shows a range [tex](2, +\infty)[/tex] is the function [tex]y=5^{x}+2[/tex] so that's the answer.
