Question

The table below shows points on the graphs of functions f andg

x        f(x)      g(x)


 -2      8        4
-1       6        3
0        8        4
1        14       7
Determine which transformation occurred on function f to get function g.

Answer 1

Vertical Compression

Explanation:

If y = f(x), then y = a×f(x) gives a vertical stretch when a > 1 and a vertical compression when 0 < a < 1.

For this question, each new point is 1/2 of the old point, meaning that a is 1/2.

Since 1/2 is a and 0 < a < 1, the transformation that occurred on the function f to get function g is a vertical compression.

Answer 2

You see that

`f(-2)=8=2\cdot 4=2 g(-2),\\ f(-1)=6=2\cdot 3=2 g(-1),\\ f(0)=8=2\cdot 4=2 g(0),\\ f(1)=14=2\cdot 7=2 g(1)`.

This rule gives you an oportunity to state that
`f(x)=2g(x)`. Therefore,
`g(x)=(1)/(2) f(x)`. Multiplying function f(x) by factor 1/2 you obtain function g(x) that is compression function f(x) in the y-direction.

Answer: compression function f(x) in the y-direction by factor 1/2.