Question

If you horizontally compress the exponential function f(x) = 2x by a factor of 3, which of these is the equation of the new function???????

A. f(x) = 6x
B. f(x) = 2(3x)
C. f(x) = 5x
D. f(x) = 3(2x)

Answer 1

Your answer would be A.

Answer 2

Option: B is the correct answer.

The equation of the new function is:

B. f(x) = 2^{3x}

Explanation:

For a given function f(x) the transformed function:

g(x)=f(bx) gives a horizontal compression or stretch depending on b

if b>1 then the graph is compressed.

and if 0 < b <1 then the graph is stretched.

We are given a parent function f(x) as:

`f(x)=2^x`

Here we have b=3

Hence, the equation of the new function will be:

`f(3x)=f(x)=2^(3x)`

Hence, the correct answer is : Option: B