Final answer:
The graph of g(x) = f(4x) given that f(x) = x^2 is a vertically stretched parabola by a factor of 16, which makes it narrower than the graph of f(x).
Step-by-step explanation:
The student has asked about finding the graph of the function g(x) = f(4x) given that f(x) = x2. To graph g(x), we need to apply the transformation that occurs when we replace x with 4x in f(x). The graph of f(x) = x2 is a parabola with its vertex at the origin (0,0) that opens upward. When we replace x with 4x, the graph of g(x) = (4x)2 = 16x2 is a parabola that is vertically stretched by a factor of 16, which means it is narrower than the original parabola f(x).
To graph g(x), you would start by plotting the original parabola f(x), labeling the graph with the functions f(x) and the variable x. Then, you apply the transformation to f(x) to create the new graph, making sure to scale the x and y axes with the maximum x and y values.