begin by graphing the square root function, ( f(x)=sqrt{x} ). then, use transformations of this graph to…
begin by graphing the square root function, ( f(x)=sqrt{x} ). then, use transformations of this graph to graph the given function.\n\n( g(x)=\frac{1}{2} sqrt{x - 4} )\n\nchoose the correct graph of ( g(x) ) below.
Answer
Explanation:
Step1: Analyze the horizontal shift
For the function (y = f(x - h)), it is a horizontal shift of (y = f(x)) by (h) units to the right. For (g(x)=\frac{1}{2}\sqrt{x - 4}), compared to (f(x)=\sqrt{x}), here (h = 4). So the graph of (y=\sqrt{x}) is shifted 4 units to the right.
Step2: Analyze the vertical compression
For the function (y=af(x)) where (0\lt a\lt1), it is a vertical compression of (y = f(x)). For (g(x)=\frac{1}{2}\sqrt{x - 4}), (a=\frac{1}{2}). So the graph of (y = \sqrt{x-4}) (after horizontal - shift) is vertically compressed by a factor of (\frac{1}{2}).
The graph of (y=\sqrt{x}) has a starting point at ((0,0)). After shifting 4 units to the right (for (y = \sqrt{x - 4})), the starting point is ((4,0)). After vertical - compression (for (y=\frac{1}{2}\sqrt{x - 4})), the (y) - values of the points on the graph of (y=\sqrt{x - 4}) are halved.
Answer:
C.