Question

PLease, I need your help plz! If you can help me I will be so pleased!

The table below shows points on the graphs of functions f and g.
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.

A. horizontal compression
B. vertical stretch
C. vertical compression
D. horizontal stretch

Answer 1

c. vertical compression.

Explanation: [(none(Have A Good Day)]

Answer 2

C. vertical compression

Explanation:

`\left\begin{array}{ccc}f(-2)=8\\g(-2)=4\end{array}\right\}\Rightarrow g(x)=(1)/(2)f(x)\\\\\left\begin{array}{ccc}f(-1)=6\\g(-1)=3\end{array}\right\}\Rightarrow g(x)=(1)/(2)f(x)\\\left\begin{array}{ccc}f(0)=8\\g(0)=4\end{array}\right\}\Rightarrow g(x)=(1)/(2)f(x)\\\left\begin{array}{ccc}f(1)=14\\g(1)=7\end{array}\right\}\Rightarrow g(x)=(1)/(2)f(x)`

`\large\boxed{g(x)=(1)/(2)f(x)}`

f(x - b) - shifted b units to the right

f(x + b) - shifted b units to the left

f(x) + b - shifted b units up

f(x) - b - shifted b units down

f(-x) - reflected across the y -axis

-f(x) - reflected across the x -axis

f(nx) - a horizontal compression by a factor of n

f(x/n) -a horizontal stretch by a factor of n

nf(x) - a vertical stretch by a factor of n

f(x)/n - a vertical compression by a factor of n