Question

If you vertically compress the square root parent function f(x) = ^x, by 1/2 of a unit what is the equation of the new function

Answer 1

The equation of the new function is
`g(x) = (√(x))/(2)`

Explanation:

Suppose we have a function f(x).

a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.

f(x - a) is shifting f(x) a units to the right.

f(x + a) is shifting f(x) a units to the left

In this question:

`f(x) = √(x)`

Vertically compressing by 1/2:

This is the same as multiplying the function by 1/2. So

`(1)/(2) * √(x) = (√(x))/(2)`

The equation of the new function is
`g(x) = (√(x))/(2)`