Answer:
Option (2)
Step-by-step explanation:
Parent function has been given as,
f(x) = [tex]\sqrt{x}[/tex]
When translated by 3 units left,
f(x + 3) = [tex]\sqrt{(x+3)}[/tex]
g(x) = [tex]\sqrt{(x+3)}[/tex]
If the translated function is stretched vertically by a scale factor = k
New function will be,
g'(x) = [tex]k\sqrt{(x+3)}[/tex]
Since a point (1, 4) passes lies on the transformed function.
g'(1) = [tex]k\sqrt{(1+3)}[/tex]
4 = 2k
k = 2
Therefore, transformed function represents the translation by 3 units in the negative side of the x-axis and stretched vertically by 2 units.
Option (2) will be the answer.
