Question

PLEASE HELP!!!!!!

The functions f(x) and g(x) are shown on the graph.


The graph shows a v-shaped graph, labeled f of x, with a vertex at the origin, a point at negative 1 comma 1, and a point at 1 comma 1. The graph shows another v-shaped graph, labeled g of x, which has a narrower opening than f of x, with a vertex at the origin, a point at negative 1 comma 2, and a point at 1 comma 2.



What transformation of f(x) will produce g(x)?


g(x) = −2f(x)

g(x) = 2f(x)

g of x equals negative one-half times f of x

g of x equals f of one-half times x

Answer 1

g(x) = f(1/2x)

Explanation:

Look at the graphs, pick a y value and see how x changes from f(x) to g(x) for the same y value.

For example, see the points at y= 2.

You can see that when f(x)=2, x = 2

And when g(x)=2, x = 1

1 is half of 2 so the x in f(x) is multiplied by half to get x for g(x).

You can verify by picking another point such as y=6.

For function f, x= 6.

For function g, x= 3.

Again 3 is half of 6 so g(x) = f(1/2 x).