Answer:
The equation of the new function is [tex]g(x) = \frac{\sqrt{x}}{2}[/tex]
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:
[tex]f(x) = \sqrt{x}[/tex]
Vertically compressing by 1/2:
This is the same as multiplying the function by 1/2. So
[tex]\frac{1}{2} \times \sqrt{x} = \frac{\sqrt{x}}{2}[/tex]
The equation of the new function is [tex]g(x) = \frac{\sqrt{x}}{2}[/tex]
