The options 2 and 4 would have the same graphical representation.
Step-by-step explanation:
Step 1:
To determine which functions are equal to the question, we must assign values to x and see which values equal the function f(x) = [tex]16.2^{x}[/tex].
Any random value can be assigned to x but the same value of x must be assigned to all the equations.
Step 2:
If we substitute x = 5, we get
Question; f(x) = [tex]16.2^{x} = 16.2^{5}= 16.(32) = 512.[/tex]
Option 1; f(x) [tex]= 4.4^{x} = 4.4^{5} = 4.(1,024)= 4,096.[/tex]
Option 2; f(x) = [tex]4.2^{x+2} = 4.2^{5+2} = 4.(128) = 512.[/tex]
Option 3; f(x) = [tex]32^{x} = 32^{5} = 33,554,432.[/tex]
Option 4; f(x) [tex]= \frac{1}{4}. 2^{x+6} = \frac{1}{4}. (2^{5+6}) =\frac{1}{4}. (2048) = 512.[/tex]
So options 2 and 4 would have the same graphical representation.
