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

The equation of the new function is

Step-by-step 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:

Vertically compressing by 1/2:

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

The equation of the new function is

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,