Given the table for a linear function
f(x)={(-2,-1),(-1,1),(0,3),(1,5)}
Need to find g(x)=-f(x)-2
First step is to find f(x) in analytical form.
The slope-intercept form would be convenient because we can find both the slope and y-intercept.
In a typical linear function
f(x)=mx+c
m= slope, can be found by (y2-y1)/(x2-x1)
c= y-intercept [value of y when x=0]
So here, taking points (0,3),(1,5)
m=(5-3)/(1-0)=2
c=3 [y-value when x=0]
=>
f(x)=2x+3
=>
g(x)
=-f(x)-2 [given]
=-(2x+3)-2 [don't forget the parentheses]
=-2x-3-2
=-2x-5
Finally
g(-2)=-2(-2)-5=4-5=-1
g(-1)=-2(-1)-5=2-5=-3
g(0)=-2(0)-5=0-5=-5
g(1)=-2(1)-5=-2-5=-7
...
