The given function is:
It is required to find the graph of g(x)=1/3 f(x).
Recall that the graph of a function g(x)=a f(x) is derived as a result of vertically shrinking the graph of f(x) towards the x-axis, where 0
Notice that in this case, a=1/3, which falls in the given interval for a vertical shrink.
Start with the graph of f(x)=x², which is the parent function for a quadratic function (graph in red):
Next, vertically shrink this graph towards the x-axis by a factor of 1/3 to graph, g(x)=1/3 f(x) in blue:
Notice that the graph that matches this from the options is the graph in option D.
The correct answer is option D.
