Answer:
Option B is correct.
[tex]f(x) = (\frac{3}{4})^x+5[/tex]
Step-by-step explanation:
Exponential function: An exponential is of the form: [tex]f(x) = ab^x[/tex]
where a is the initial value and b is the growth factor
If b> 1, then the function is an exponential growth function.
if 0<b< 1 , then the function is an exponential decay function.
The function which is represented in the graph is exponential decay function.
The parent function [tex]f(x) = (\frac{3}{4})^x[/tex] represents the exponential function.
Vertical shift:
If c is a positive real number , then the graph y= f(x)+c is the graph of y =f(x) shifted c units upward.
If c is a positive real number , then the graph y= f(x)-c is the graph of y =f(x) shifted c units downward.
Then;
The graph [tex]f(x) = (\frac{3}{4})^x+5[/tex] is the graph of [tex]f(x) = (\frac{3}{4})^x[/tex] is shifted 5 units up.
Therefore, the function which represented in the graph is [tex]f(x) = (\frac{3}{4})^x+5[/tex]
