Question

Which statement describes the graph of g(x) with respect to the graph of f(x)?

orange line is the f(x)
the purple line is the g(x)





























It is translated right 3 units.

It is compressed horizontally by a factor of 3.

It is translated up 3 units.

It is stretched vertically by a factor of 3.

Answer 1

The correct option regarding the transformation of graph g(x) with respect to the parent function f(x) is:

It is stretched vertically by a factor of 3.

Explanation:

We could see that the vertex of the graph of function g(x) is same as that of f(x).

This means that there is no shift of the graph of f(x) either to the left or to the right or top and bottom.

Also, we could observe that at x=0 f(x)=4

and at x=0 g(x)=12

This means that the graph of g(x) is stretched vertically by a factor of 3.

Answer 2

The vertex of the two functions is in the same place, so there is no translation involved. Point (0, 4) on f(x) is point (0, 12) on g(x).

The appropriate choice seems to be ...
It is stretched vertically by a factor of 3.