Question

If you horizontally compress the exponential function (x) = 2 by a factor of3, which of these is the equation of the new function?A. f(x) = 6%B. f(x) = 3(2)C. f(x) = 5D. fx) = 2(8

Answer 1

As per given by the quetion,

The given exponential function is,

`f(x)=2^x_{^{}}`

Now,

From the concept of compression.

When we compress the function, y=f(x) by scale factor k, where k>1, then the function after compression will become;

`y=f(kx)`

So,

From the given function,

`f(x)=2^x`

And, the scale factor is given that ,

`k=3`

Then,

From concept of compression,

`\begin{gathered} y=f(kx) \\ y=f(3x) \\ f(3x)=2^((3x)) \end{gathered}`

Hence, the option D is correct.