graph each function.\n$y = 2sqrt{x + 2}$
graph each function.\n$y = 2sqrt{x + 2}$
Answer
Explanation:
Step1: Find the domain
For the function (y = 2\sqrt{x + 2}), the expression under the square - root must be non - negative. So, (x+2\geq0), which gives (x\geq - 2).
Step2: Find some key points
When (x=-2), (y = 2\sqrt{-2 + 2}=0). When (x=-1), (y = 2\sqrt{-1 + 2}=2). When (x = 2), (y=2\sqrt{2 + 2}=2\times2 = 4).
The function (y = 2\sqrt{x + 2}) is a transformation of the parent function (y=\sqrt{x}). The parent function (y = \sqrt{x}) has a domain (x\geq0) and passes through ((0,0)), ((1,1)), ((4,2)). The function (y = 2\sqrt{x + 2}) is a horizontal shift of (y=\sqrt{x}) to the left by 2 units (because of (x+2)) and a vertical stretch by a factor of 2 (because of the coefficient 2 in front of the square - root).
The first graph (with the domain starting at (x=-2)) is the correct graph of (y = 2\sqrt{x+2}).
Answer:
The first graph (the one with the domain starting at (x =-2)) is the correct graph of the function (y = 2\sqrt{x + 2}).