use transformations of ( f(x)=x^{2} ) to graph the following function.\n\n( g(x)=x^{2}+4 )\n\nuse the…

Explanation:

Step1: Recall the transformation rule

For a function (y = f(x)+k), if (k>0), the graph of (y = f(x)) is shifted up by (k) units. Here (f(x)=x^{2}) and (k = 4), so the graph of (g(x)=x^{2}+4) is the graph of (y=x^{2}) shifted up by 4 units.

Step2: Analyze key points of (y=x^{2})

The vertex of (y = x^{2}) is ((0,0)). For (y=x^{2}), when (x = 1), (y=1); when (x=- 1), (y = 1).

Step3: Apply the transformation to key points

For (g(x)=x^{2}+4), the vertex ((0,0)) of (y=x^{2}) is transformed to ((0,0 + 4)=(0,4)). When (x = 1), (g(1)=1^{2}+4=5); when (x=-1), (g(-1)=(-1)^{2}+4=5).

Answer:

Graph the parabola (y = x^{2}) (a U - shaped curve with vertex at ((0,0))) and then shift it up by 4 units. The vertex of (y=x^{2}+4) is ((0,4)) and it passes through the points ((1,5)), ((-1,5)) etc.