Question

The graph of the function f(x) = x2 is shown. Compared to this, how would the graph of a function g appear, if g(x) = f(2x)?

please answer ASAP.

A) The graph of g would reflect in the line x = 2.
B) The graph of g would be wider.
C) The graph of g would shift 2 units up.
D) The graph of g would be narrower.

Answer 1

D) The graph of g would be narrower.

Explanation:

`f(x)=x^(2)`

`g(x)=f(2x)=(2x)^(2)=(2)^(2) \cdot (x)^(2)=4x^(2)`

You have to make a rough graph to check the results of transformation. For that graph of both
`x^(2)` and
`4x^(2)` is attached with the answer.

For thinking like that, just see that in the
`4x^(2)` as compared to
`x^(2)`, you are multiplying each value by 4, it means you are increasing each the value so every point should move up by a factor of 4. But one point is fixed which is the bottom point as its value is zero initially and after multiplying it by 4 it won't change as 0×4=0. So graph will become narrow