Question

Graph transformation of the following line given the transformation: g(x)= -f(x) -2

Answer 1

Transformation of a Function

We are given the function:

`y=f(x)=(2)/(3)x+8`

And it's required to find another function g(x) according to the transformation:

g(x) = -f(x) - 2

First, we calculate the negative of f(x):

`-f(x)=-((2)/(3)x+8)=-(2)/(3)x-8`

And now we subtract 2 to find g(x):

`g(x)=-(2)/(3)x-8-2=-(2)/(3)x-10`

The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10

Answer:

`g(x)=-(2)/(3)x-10`