Transformation of a Function
We are given the function:
[tex]y=f(x)=\frac{2}{3}x+8[/tex]
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):
[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]
And now we subtract 2 to find g(x):
[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]
The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10
Answer:
[tex]g(x)=-\frac{2}{3}x-10[/tex]
