The given function is:
[tex]g(x)=\frac{1}{4}x-3[/tex]
To graph the function we can make a table of values, by replacing different x-values into the function and finding g(x) as follows:
[tex]\begin{gathered} x=0 \\ g(0)=\frac{1}{4}*0-3=-3 \\ x=-1 \\ g(-1)=\frac{1}{4}*(-1)-3=-\frac{1}{4}-3=\frac{-1-12}{4}=-\frac{13}{4} \\ x=1 \\ g(1)=\frac{1}{4}*1-3=\frac{1}{4}-3=\frac{1-12}{4}=-\frac{11}{4} \end{gathered}[/tex]
We can apply the same procedure and we're going to obtain the following table of values:
These are the coordinates of the points we have to sketch in the graph, and this looks like this:
