Answer:
The function [tex]a)f(x)=5(\frac{5}{2})^{x}[/tex] is which is represented by the graph shown.
Step-by-step explanation:
As the graph is depicted in the interval (-1, 10), you should give values to each function within this interval to know which is the correct function.
1. When x=0, as any number raised to zero gives one, all functions will have the value 5 as a result
[tex]a)f(x)=5(\frac{3}{5})^{0}\\f(x)=5(1)\\f(x)=5[/tex]
[tex]b)f(x)=5(\frac{5}{2})^{0}\\f(x)=5(1)\\f(x)=5[/tex]
[tex]c)f(x)=5(\frac{2}{5})^{0}\\f(x)=5(1)\\f(x)=5[/tex]
[tex]d)f(x)=5(\frac{5}{3})^{0}\\f(x)=5(1)\\f(x)=5[/tex]
2. When x=1
[tex]a)f(x)=5(\frac{3}{5})^{1}\\f(x)=5(\frac{3}{5})\\f(x)=3[/tex]
[tex]b)f(x)=5(\frac{5}{2})^{1}\\f(x)=\frac{25}{2}[/tex]
[tex]c)f(x)=5(\frac{2}{5})^{1}\\f(x)=5(\frac{2}{5})\\f(x)=2[/tex]
[tex]d)f(x)=5(\frac{5}{3})^{1}\\f(x)=5(\frac{5}{3})\\f(x)=\frac{25}{3}[/tex]
You could continue giving values to x to find the other values that the function takes but it is not necessary because as you can see the only function that gives the value f(x)=2 when x=1 is the third one, therefore the function [tex]a)f(x)=5(\frac{5}{2})^{x}[/tex] is which is represented by the graph shown.
