Question

Which graph represent the function f(x)=4x^2

Answer 1

The graph of the function
`f(x)=4x^2` is a transformation of the graph of the parent function
`f(x)=x^2`; more precisely, the graph of the function
`f(x)=4x^2` is the graph of the function
`f(x)=x^2` compressed by a factor of 4 in the
`x` direction.

Remember that we can compress or stretch the graph of a function in the
`x` direction by multiplying
`x` by a constant
`c`.
if
`c\ \textgreater \ 1`, we are compressing the graph in the
`x` direction.
if
`0\ \textless \ c\ \textless \ 1`, we are stretching the graph in the
`x` direction.

We can conclude that the graph of the function
`f(x)=4x^2` is the graph in the first picture. Also, in the second picture you will see the graph of both the function and its parent function simultaneously.