Question

Which of the following would have the same graphic representation as the function f(x)=16(2)^x

Answer 1

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) = $16.2^{x}$.

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) = $16.2^{x} = 16.2^{5}= 16.(32) = 512.$

Option 1; f(x) $= 4.4^{x} = 4.4^{5} = 4.(1,024)= 4,096.$

Option 2; f(x) = $4.2^{x+2} = 4.2^{5+2} = 4.(128) = 512.$

Option 3; f(x) = $32^{x} = 32^{5} = 33,554,432.$

Option 4; f(x) $= \frac{1}{4}. 2^{x+6} = \frac{1}{4}. (2^{5+6}) =\frac{1}{4}. (2048) = 512.$

So options 2 and 4 would have the same graphical representation.